Solitons

Dipole and quadrupole solitons in a two-dimensional optically induced defocusing photonic lattice are theoretically predicted and experimentally observed. It is shown that in-phase nearest-neighbor and out-of-phase next-nearest-neighbor dipoles exist and can be stable in the intermediate intensity regime. There are also different types of dipoles that are always unstable. In-phase nearest-neighbor quadrupoles are also numerically obtained, and may also be linearly stable. Out-of-phase, nearestneighbor quadrupoles are found to be typically unstable. These numerical results are found to be aligned with the main predictions obtained analytically in the discrete nonlinear Schrödinger model. Finally, experimental results are presented for both dipole and quadrupole structures, indicating that self-trapping of such structures in the defocusing lattice can be realized for the length of the nonlinear crystal (10 mm).

A. Muñoz Mateo1,3,∗ Xiaoquan Yu2,3,† and Jun Nian4,5‡ 1 Departament de Fı́sica Quàntica i Astrofı́sica, Universitat de Barcelona, Martı́ i Franquès, 1, E–08028 Barcelona, Spain 2 Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin, New Zealand 3New Zealand Institute for Advanced Study, Centre for Theoretical Chemistry and Physics,Massey University, Auckland 0745, New Zealand 4Institut des Hautes Études Scientifiques, Le Bois-Marie, 35 route de Chartres, 91440 Bures-sur-Yvette, France and 5C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, NY 11794-3840, United States

We consider the thermal expansion, change of sound velocity with pressure and temperature, and the Poisson ratio of lattices which have rigid units (polyhedra very large stiffness to change in bond-length and to bondangle variations) connected to other such units through relatively compressible polyhedra. We show that in such a model, the potential energy for rotations of the rigid units can occur only as a function of the combination Θi ≡ (θi -(∇ × ui)/2), where θi are the orthogonal rotation angles of the rigid unit i and ui is its displacement. Given such new invariants in the theory of elasticity and the hierarchy of force constants of the model, a negative thermal expansion coefficient as well as a decrease in the elastic constants of the solid with temperature and pressure is shown to follow. These are consistent with the observations.

In the low-energy regime, the Su-Schrieffer-Heeger (SSH) model's key characteristics are encapsulated by a Dirac-type Hamiltonian in continuum space, i.e., localized states emerge at the boundaries. Building on this, we have developed an effective Hamiltonian to model ultracold interacting bosons on an SSH-like lattice through variational minimization under the mean-field approximation. To pinpoint the boundary states, we have developed an algorithm by generalizing the imaginary time propagator, where an initial state evolves under the squared Hamiltonian to converge to the targeted state. This algorithm has broader applicability, enabling the identification of specific eigenstates in various contexts. Furthermore, we draw a parallel to an experimentally physical setup involving a gas of ultracold bosons confined to an array of potential wells with alternating depths. By establishing the system's analogy with the SSH system, we apply our algorithm to investigate boundary states in the presence of interactions, demonstrating how these findings align with those of the continuous system.

In zero magnetic field the superconductor Sr2RuO4 is believed to have a chiral spin triplet pairing state in which the gap function d-vector is aligned along the crystal c-axis. Using a phenomenological but orbital specific description of the spin dependent electron-electron attraction and a realistic quantitative account of the electronic structure in the normal state we analyze the orientation of the spin triplet Cooper pair d-vector in response to an external c-axis magnetic field. We show that for suitable values of the model parameters a c-axis field of only 20 mT is able to cause a reorientation phase transition of the d-vector from along c to the a -b plane, in agreement with recent experiments.

The paper reviews recent work on time reversal symmetry (TRS) breaking superconductors. The family of TRS breaking superconductors is growing relatively fast, with many of its newly discovered members being non-centrosymmetric. However, many of the superconductors which possess center of inversion also break TRS. The TRS is often identified by means of the muon spin relaxation effect (µSR) or/and the Kerr effect. Both methods effectively measure the spontaneous appearance of the bulk magnetic field below superconducting transition temperature. One of the systems most carefully studied so far is Sr 2 RuO 4 believed to be spin triplet chiral p-wave superconductor. This compound provides an example of the material whose many band, multi-condensate modelling has enjoyed a number of successes. We discuss in some details the properties of the material. Among them is the polar Kerr effect, which understanding has resulted in the discovery of the novel mechanism of the phenomenon. The mechanism is universal and thus applicable to all systems with multiorbital character of states at the Fermi energy.

A horizontal layer containing a miscible mixture of two fluids can generate dissipative solitons called convectons when heated from below. The physics of the system leading to this behavior is explained, and the properties of the resulting convectons are described. The convectons are shown to be present in a parameter regime known as the pinning region containing a multiplicity of stable convectons of odd and even parity. These lie on solution branches that snake back and forth across the pinning region and illustrate a phenomenon known as homoclinic snaking. Examples of single pulse and multipulse convectons in periodic and closed containers are exhibited and compared with similar states described by the Swift-Hohenberg equation. Time-dependent states in the form of localized traveling waves are computed and distinguished from convectons that drift.

Propöe-se um novo esquema de qua'ntizaçlo seml-clássi ca em teoría de campos ..a expanslo em torno da carga (ETC) +. o 'qua-fr é desenvolvido dentro do formalismo canónico. Esse método, que é apropriado para quantizar teorias Invariantes por transformaçoes de ga£ ge globais, é utilizado no tratamento da teoría logarítmica nao relativística proposta por Blalynlcki-Birula e ttycielski -a qual pode ser formulada em urn número qualquer de dimensöes espaciáis. A Equaçio de Schrodinger nao linear tambëm é quantizada por me¡o da ETC. As teorias logarítmicas clássicas, tanto a nao relativístrea quanto a re lat i vistica, sao a^tíi estudadas com bastante detalhe.-37 Além disso, mostra-se que a regra de quantizaçlo de Bohr-Sommerfeld (RQBS) em teoria de campos é, em mu i tos casos, equivalente à quantj_ zaçio da carga. Essa regra é entlo empregada no modelo de Thirring I^assivo e nas teorias logarítmicas. A RQBS corresponde a urna versao simplificada e nao local da ETC -i sto nas teorias em que esta aproximaçao se aplique.

Propöe-se um novo esquema de qua'ntizaçlo seml-clássi ca em teoría de campos ..a expanslo em torno da carga (ETC) +. o 'qua-fr é desenvolvido dentro do formalismo canónico. Esse método, que é apropriado para quantizar teorias Invariantes por transformaçoes de ga£ ge globais, é utilizado no tratamento da teoría logarítmica nao relativística proposta por Blalynlcki-Birula e ttycielski -a qual pode ser formulada em urn número qualquer de dimensöes espaciáis. A Equaçio de Schrodinger nao linear tambëm é quantizada por me¡o da ETC. As teorias logarítmicas clássicas, tanto a nao relativístrea quanto a re lat i vistica, sao a^tíi estudadas com bastante detalhe.-37 Além disso, mostra-se que a regra de quantizaçlo de Bohr-Sommerfeld (RQBS) em teoria de campos é, em mu i tos casos, equivalente à quantj_ zaçio da carga. Essa regra é entlo empregada no modelo de Thirring I^assivo e nas teorias logarítmicas. A RQBS corresponde a urna versao simplificada e nao local da ETC -i sto nas teorias em que esta aproximaçao se aplique.

We review the state of the art and recently obtained theoretical and experimental results for two-and three-dimensional (2D and 3D) solitons and related states, such as quantum droplets, in optical systems, atomic Bose-Einstein condensates (BECs), and other fields -in particular, liquid crystals. The central challenge is avoiding the trend of 2D and 3D solitary states supported by the ubiquitous cubic nonlinearity to be strongly unstable -a property far less present in one-dimensional systems. Many possibilities for the stabilization of multi-dimensional states have been theoretically proposed over the years. Most strategies involve non-cubic nonlinearities or using different sorts of potentials, including periodic ones. New important avenues have arisen recently in systems based on two-component BEC with spin-orbit coupling, which have been predicted to support stable 2D and metastable 3D solitons. An important recent breakthrough is the creation of 3D quantum droplets. These are self-sustained states existing in two-component BECs, which are stabilized by the presence of Lee-Hung-Yang quantum fluctuations around the underlying mean-field states. By and large, multi-dimensional geometries afford unique opportunities to explore the existence of complex self-sustained states, including topologically rich ones, which by their very nature are not possible in one-dimensional geometries. In addition to vortex solitons, these are hopfions, skyrmions, and hybrid vortex-antivortex complexes, which have been predicted in different models. Here we review recent landmark findings in this field and outline outstanding open challenges. 1D one-dimensional 2D two dimensional 3D three dimensional BEC Bose-Einstein condensate FF fundamental frequency GPE Gross-Pitaevskii equation GVD group-velocity dispersion LHY Lee-Huang-Yang (correction to the mean-field dynamics of BEC) MF mean field MM mixed mode NLSE nonlinear Schrödinger equation SH second harmonic SOC spin-orbit coupling SV semi-vortex TS Townes' soliton VK Vakhitov-Kolokolov (stability criterion) 4.3. Giant vortex solitons in binary BECs 4.4. Quantum droplets in binary BECs 5. Soliton states in liquid crystals and liquid ferromagnets 6. Conclusions and outlook 7. Bibliography 1.

Many coastal protection structures in the UK have been designed for storm surges with appropriate return periods but their performance during tsunami-type waves is uncertain. A shallow water and Boussinesq (referred to as SWAB) model is well suited to the investigation of both nearshore storm waves and tsunami waves. This paper makes use of the SWAB model to compare the effect on coastal structures of solitary waves and storm waves. Wave runup parameters for both types of wave are generated, and shown to be in good agreement with experimental data. The equations behind the SWAB model were derived assuming a small bed slope, and are therefore not suitable for modelling waves interacting with vertical and near-vertical structures. However, the introduction of a reverse momentum term, to take account of a jet of water typical of a breaking wave impacting against a structure, allows wave overtopping volumes to be well predicted although it had a minor effect on the forces acting on the structure. Comparisons with experimental data, both with solitary waves and storm waves, are presented. Using this model, the difference between the impact, in terms of wave forces and wave overtopping, of tsunami waves and storm waves for a given structure is investigated.

This paper analyses the advantageous features of supercontinuum (SC) generated from continuous-wave (CW) excitation. It has been shown that both the generation mechanisms and the temporal and spectral properties of supercontinuum produced with CW pump lasers are different from those of generated by means of pulsed excitation, in particular the remarkable smoothness of CW-SC spectra. We show that these unique spectral features stem from the fission of the partially coherent CW input beam into a train of subpicosecond pulses induced by the modulation instability (MI). These subpicosecond pulses lead to the formation of optical solitons with inherently random parameters, which self-frequency shift differently depending on their characteristics. The resulting supercontinuum spectrum is hence the average of many different soliton spectra, which have suffered different frequency shifts. Different experimental setups used in our lab are presented and the dependence of the SC generation on the coherence of the fiber laser and the fiber dispersion profile are shown.

the properties of compacton-anticompacton collision processes. We compare and contrast results for the case of compacton-anticompacton solutions of the K(l,p) Rosenau-Hyman (RH) equation for l=p=2, with compactonanticompacton solutions of the L(l,p) Cooper-Shepard-Sodano (CSS) equation for p=1 and l=3. This study is performed using a Padé discretization of the RH and CSS equations. We find a significant difference in the behavior of compacton-anticompacton scattering. For the CSS equation, the scattering can be interpreted as "annihilation" as the wake left behind dissolves over time. In the RH equation, the numerical evidence is that multiple shocks form after the collision, which eventually lead to "blowup" of the resulting wave form.

Extending a Padé approximant method used for studying compactons in the Rosenau-Hyman (RH) equation, we study the numerical stability of single compactons of the Cooper-Shepard-Sodano (CSS) equation and their pairwise interactions. The CSS equation has a conserved Hamiltonian which has allowed various approaches for studying analytically the nonlinear stability of the solutions. We study three different compacton solutions and find they are numerically stable. Similar to the collisions between RH compactons, the CSS compactons reemerge with same coherent shape when scattered. The time evolution of the small-amplitude ripple resulting after scattering depends on the values of the parameters l and p characterizing the corresponding CSS equation. The simulation of the CSS compacton scattering requires a much smaller artificial viscosity to obtain numerical stability than in the case of RH compacton propagation.

We present an exact analytical model of a cigar-shaped Bose-Einstein condensate at negative temperature. This work is motivated by the first experimental discovery of negative temperature in Bose-Einstein condensate by Braun et al. We have considered an external confinement which is a combination of expulsive trap, bi-chromatic optical lattice trap, and linear trap. The present method is capable of providing the exact form of the condensate wavefunction, phase, nonlinearity and gain/loss. One of the consistency conditions is shown to map onto the Schrödinger equation, leading to a significant control over the dynamics of the system. We have modified the model by replacing the optical lattice trap by a bi-chromatic optical lattice trap, which imparts better localization at the central frustrated site, delineated through the variation of condensate fraction. Estimation of temperature and a numerical stability analysis are also carried out. Incorporation of an additional linear trap in...

We study Skyrmion dynamics in a (2+1)-dimensional Skyrme model. The system contains a dimensionless parameter α, with α = 0 corresponding to the O(3) sigmamodel. If two Skyrmions collide head-on, then they can either coalesce or scatterthis depends on α and on the incident speed v, and is affected by transfer of energy to and from the internal vibrational modes of the Skyrmions. We classify these internal modes and compute their spectrum, for a range of values of α. In particular, we find that there is a fractal-like structure of scattering windows, analogous to those seen for kink-antikink scattering in 1+1 dimensions.

Experimental evidence is presented in support of the theoretical prediction of Diamessis and Redekopp [J. Phys. Oceanogr. 36, 784 (2006)] for wave-induced vortex shedding at the lower solid boundary of a stratified fluid system as a result of global instability. The time-dependent boundary layer induced by a strongly nonlinear internal wave of depression in shallow water is examined experimentally. Measurements of the velocity field close to the bottom boundary illustrate coherent periodic shedding of vortex structures at the lower boundary in the adverse pressure gradient region aft of the wave. The vortical structures ascend high into the water column and cause significant benthic turbulence. It is shown that global instability has a critical threshold dependent on the Reynolds number of the flow and the amplitude of the wave. The critical amplitudes observed are approximately half that predicted by Diamessis and Redekopp [J. Phys. Oceanogr. 36, 784 (2006)], indicating that intern...

We study two coupled systems of nonlinear partial differential equations, namely, generalized Boussinesq-Burgers equations and 2 1 -dimensional Davey-Stewartson equations. The Lie symmetry method is utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the 2 1dimensional Davey-Stewartson equations.

We develop an analytical procedure to compute all relevant physical properties of scalar field oscillons in models with quartic polynomial potentials: energy, radius, frequency, core-amplitude, and lifetime. We compare our predictions to numerical simulations of models with symmetric and asymmetric double well potentials in three spatial dimensions, obtaining excellent agreement. We also explain why oscillons have not been seen to decay in two spatial dimensions.

We investigate the matching between (1+1)-dimensional nonlinear field theories coupled to an external stochastic environment and their lattice simulations. In particular, we focus on how to obtain numerical results which are lattice-spacing independent, and on how to extract the correct effective potential which emerges from the simulations. As an application, we study the thermal production of kink-antikink pairs, obtaining a number density of pairs which is lattice-spacing independent and the effective barrier for pair production, i.e., the effective kink mass.

In this paper an infinite system of a Toeplitz matrix was considered and some results are demonstrated as partially new solution for the system. A survey was conducted on infinite system based on Toeplitz matrix computation. A unique solution of Markov chains is presented with some advance technique of canonical solution. Markov chains can be exploited as the basis of stable algorithms , for the computation of the solution of the nonlinear matrix. Computational integrals are carried out with operations involved in infinite Toeplitz matrix system. In this work, the integral solution of Markov chains of nonlinear matrix equations are presented.

En la obra El Derecho de la Sociedad, Niklas Luhmann sostuvo que el acoplamiento estructural de los subsistemas Derecho y Política se realiza por medio de la Constitución, así como que el acoplamiento estructural entre los subsistemas Derecho y Economía se realiza por medio del contrato o la propiedad privada; sin embargo, la revisión del concepto de regulación y la identificación de su núcleo jurídico, sugiere que, a diferencia de la propuesta de Luhmann, la regulación es el principal acoplamiento estructural entre el subsistema Derecho y todos los demás subsistemas sociales, pues sirve de comunicación entre los subsistemas sin alterar su diferenciación, autonomía en su autopoiesis, códigos y autorreferencia. A partir de esta precisión, el Derecho debe ser considerado en todos los estudios interdisciplinarios con epistemología sistémica, pues el Derecho, al regular, se acopla a cada subsistema social.

Abstract:
In the work The Law of Society, Niklas Luhmann argued that the structural coupling of the Legal and Political subsystems is realized by means of the Constitution, as well as that the structural coupling between the Legal and Economic subsystems is realized by means of the contract or private property; however, the review of the concept of regulation and the identification of its legal core suggests that, unlike Luhmann's proposal, regulation is the main structural coupling between the legal subsystem and all other social subsystems, as it serves as communication between the subsystems without altering their differentiation, autonomy in their autopoiesis, codes and self-reference. Based on this precision, law should be considered in all interdisciplinary studies with systemic epistemology, because law, when regulating, is coupled to each social subsystem.

In this paper we study the propagation of solitons in a Bose-Einstein condensate governed by the time dependent one dimensional Gross-Pitaevskii equation managed by Feshbach resonance in a linear external potential. We give the Lax pair of the Gross-Pitaevskii equation in Bose-Einstein condensates and obtain exact N-soliton solution by employing the simple, straightforward Darboux transformation. As an example, we present exact one and two-soliton solution and discuss their transmission, interaction and dynamic properties. We further calculate the particle number, momentum and energy of the solitons and discuss their conservation laws. Knowledge of soliton dynamics helps us in understanding the physical nature of the condensate and in the calculation of the thermodynamic properties.

The construction of a family of real Hamiltonian forms (RHF) for the special class of affine 1 + 1-dimensional Toda field theories (ATFT) is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is generalized to infinitedimensional Hamiltonian systems. The construction method is illustrated on the explicit nontrivial example of RHF of ATFT related to the exceptional algebras E 6 and E 7 . The involutions of the local integrals of motion are proved by means of the classical R-matrix approach.

Bu çalışmada, Baryum titanat (BaTiO3) nanofiber ve nanotozlar elektroeğirme yöntemiyle üretilmiştir. Nanofiberler 800 °C sıcaklıkta ısıl işleme tabi tutularak barium titanat nanotoz elde edilmiştir. Elde edilen numunelerin mikroyapı analizleri XRD ve SEM ile yapılmıştır. Isıl işlem öncesi SEM görüntülerine göre ortalama 800 nm çapa sahip düzgün silindirik fiberler elde edilmiştir. Isıl işlem sonrasındaki SEM görüntülerinde ise 50-250 nm aralığında çapa sahip düzgün ve homojen yapıdaki küresel baryum titanat tozların elde edildiği bulunmuştur. XRD analiz sonuçları BaTiO3 nanotozların kübik kristal yapıda olduğunu göstermiştir.

Saktioto and Prof. Dr. Jalil Ali for all their guidance and support throughout the duration of this research and thesis writing. I am greatly indebted to them for the knowledge imparted and the precious time they allocated to guide me. Dr. Saktioto provided the overall framework of this studies. I would like to extend my sincere appreciation to my family especially mom and dad for their tender support, morally and financially. I would also like to thanks to members of the Institute of Advanced Photonics and Sciences (APSI) for their assistance. They had provided me with ample information, cooperation and help during the process of conducting my research.

RESUMO Um problema recorrente em computação científica é resolver numericamente proble-mas de propagação de ondas em que o domínio original do problema é truncado via uma condição de fronteira artificial. As reflexões causadas pela imposição dessa fron-teira devem ser atenuadas, de modo que as ondas refletidas não voltem para o interior do domínio. Neste trabalho, fazemos uma revisão sobre as condições de contorno ab-sorventes (ABCs) para uma equação da onda clássica, bem como a formulação de ABCs exatas não-locais e as ABCs aproximadas de Engquist e Majda. Ademais, ex-planaremos sobre aspectos teóricos das ABCs de Engquist e Majda, como análise de estabilidade e convergência, de forma a estimular e elucidar a construção de novas ABCs. ABSTRACT A common problem in scientific computing is to numerically solve problems related to wave propagation. Basically the original domain is truncated by an artificial boundary condition that can generate reflexions caused by the force-placement o...

This study investigates the stability and decay properties of solutions to nonlinear Schrödinger equations (NLSEs) with time-dependent coefficients. Employing a blend of analytical and numerical methods, we delve into how temporal variations in coefficients influence the dynamics of wave functions. Our analysis reveals that time-dependent coefficients significantly affect the stability and decay rates of solutions, uncovering conditions that lead to either enhanced stability or accelerated decay. The findings highlight the critical role of coefficient temporality in dictating the behavior of NLSE solutions. These insights not only advance our theoretical understanding of NLSEs but also bear implications for practical applications in fields modeled by these equations. Our research opens avenues for exploiting time-dependent behaviors in designing systems with desired dynamical properties.

Nonlocal quantum fluids emerge as dark-matter models and tools for quantum simulations and technologies. However, strongly nonlinear regimes, like those involving multi-dimensional selflocalized solitary waves (nonlocal solitons), are marginally explored for what concerns quantum features. We study the dynamics of 3D+1 solitons in the second-quantized nonlocal nonlinear Schrödinger equation. We theoretically investigate the quantum diffusion of the soliton center of mass and other parameters, varying the interaction length. 3D+1 simulations of the Ito partial differential equations arising from the positive P-representation of the density matrix validate the theoretical analysis. The numerical results unveil the onset of non-Gaussian statistics of the soliton, which may signal quantum-gravitational effects and be a resource for quantum computing. The non-Gaussianity arises from the interplay of the quantum diffusion of the soliton parameters and the stable invariant propagation. The...

The generation of finite energy packets of X-waves is analysed in normally dispersive cubic media by using an X-wave expansion. The 3D nonlinear Schroedinger model is reduced to a 1D equation with anomalous dispersion. Pulse splitting and beam replenishment as observed in experiments with water and Kerr media are explained in terms of a higher order breathing soliton. The results presented also hold in periodic media and Bose-condensed gases.

Plane waves in Kerr media spontaneously generate paraxial X-waves (i.e. non-dispersive and non-diffractive pulsed beams) that get amplified along propagation. This effect can be considered a form of conical emission (i.e. spatio-temporal modulational instability), and can be used as a key for the interpretation of the out of axis energy emission in the splitting process of focused pulses in normally dispersive materials. A new class of spatio-temporal localized wave patterns is identified. X-waves instability, and nonlinear X-waves, are also expected in periodical Bose condensed gases.

We predict that an ultra-cold Bose gas in an optical lattice can give rise to a new form of condensation, namely matter X waves. These are non-spreading 3D wave-packets which reflect the symmetry of the Laplacian with a negative effective mass along the lattice direction, and are allowed to exist in the absence of any trapping potential even in the limit of non-interacting atoms. This result has also strong implications for optical propagation in periodic structures.

The nonlinear propagation of light pulses in liquid-filled photonic crystal fibers is considered. Due to the slow reorientational nonlinearity of some molecular liquids, the nonlinear modes propagating inside such structures can be approximated, for pulse durations much shorter than the molecular relaxation time, by temporally highly-nonlocal solitons, analytical solutions of a linear Schrödinger equation. The physical relevance of these novel solitary structures, which may have a broad range of applications, is discussed and supported by detailed numerical simulations.

We observe the formation of an intense optical wavepacket fully localized in all dimensions, i.e. both longitudinally (in time) and in the transverse plane, with an extension of a few tens of fsec and microns, respectively. Our measurements show that the self-trapped wave is a X-shaped light bullet spontaneously generated from a standard laser wavepacket via the nonlinear material response (i.e., second-harmonic generation), which extend the soliton concept to a new realm, where the main hump coexists with conical tails which reflect the symmetry of linear dispersion relationship.

One of the extraordinary aspects of nonlinear wave evolution which has been observed as the spontaneous occurrence of astonishing and statistically extraordinary amplitude wave is called rogue wave. We show that the eigenvalues of the associated equation of nonlinear Schrödinger equation are almost constant in the vicinity of rogue wave and we validate that optical rogue waves are formed by the collision between quasi-solitons in anomalous dispersion fiber exhibiting weak third order dispersion.

We propose a novel configuration that utilizes electromagnetically induced transparency (EIT) to tailor a fiber mode propagating inside a thin optical fiber and coherently control its dispersion properties to drastically reduce the group velocity of the fiber mode. The key to this proposal is: the evanescent-like field of the thin fiber strongly couples with the surrounding active medium, so that the EIT condition is met by the medium. We show how the properties of the fiber mode are modified due to the EIT medium, both numerically and analytically. We demonstrate that the group velocity of the new modified fiber mode can be drastically reduced (≈44 m/sec) using the coherently prepared orthohydrogen doped in a matrix of parahydrogen crystal as the EIT medium.

Suppression of the quantum-mechanical collapse by repulsive interactions 11:40-12:10 Goran Gligoric The effect of dipole-dipole interaction on transition from the immiscible to miscible state in linearly coupled binary dipolar Bose-Einstein condensate 12:10-12:40 Alexander Itin Many-particle Landau-Zener models and dynamics of quantum phase transitions

We report on the first observation of surface gap solitons, a nonlinear optical analog of localized surface Tamm states in periodic electronic potentials. We demonstrate strong beam self-trapping in the form of staggered surface modes at the interface between uniform and periodic dielectric media with defocusing nonlinear response.

In the present work, by employing the field equations given in [15] and the extended PLK method derived in [9], we have studied the head-on collision of solitary waves in arteries. Introducing a set of stretched coordinates which include some unknown functions characterizing the higher order dispersive effects and the trajectory functions to be determined from the removal of possible secularities that might occur in the solution. Expanding these unknown functions and the field variables into power series of the smallness parameter and introducing the resulting expansions into the field equations we obtained the sets of partial differential equations. By solving these differential equations and imposing the requirements for the removal of possible secularities we obtained the speed correction terms and the trajectory functions. The results of our calculation show that both the evolution equations and the phase shifts resulting from the head-on collision of solitary waves are quite different from those of Xue [15], who employed the incorrect formulation of Su and Mirie [4]. As opposed to the result of previous works on the same subject, in the present work the phase shifts depend on the amplitudes of both colliding waves.

We present a new description of nonequilibrium square patterns as a harmonically coupled crystal lattice. In a vertically oscillating granular layer, different transverse normal modes of the granular square-lattice pattern are observed for different driving frequencies (f d) and accelerations. The amplitude of a mode can be further excited by either frequency modulation of f d or reduction of friction between the grains and the plate. When the mode amplitude becomes large, the lattice melts (disorders), in accord with the Lindemann criterion for melting in two-dimensions.

Electron Spin-Echo @SE) measurements on mixed-stack charge transfer compound tetrathiafulvalene ('fTF)-chloranil (CA) are reported. Below Neutral-Ionic transition temperature, the ESE signals related to the spin solitons were observed. Comparing the phase memory time with the inverse of the EPR line-width, it was found that a crossover from fast motion of the spin solitons to slow motion took place around 70K. In addition, the spin-lattice relaxation measurements suggested the thermal fluctuation of the dimerized lattice above 60K.

We investigate numerically the scattering of a moving discrete breather on a pair of junctions in a Fermi-Pasta-Ulam chain. These junctions delimit an extended region with different masses of the particles. We consider ͑i͒ a rectangular trap, ͑ii͒ a wedge shaped trap, and ͑iii͒ a smoothly varying convex or concave mass profile. All three cases lead to DB confinement, with the ease of trapping depending on the profile of the trap. We also study the collision and trapping of two DBs within the profile as a function of trap width, shape, and approach time at the two junctions. The latter controls whether one or both DBs are trapped.

We study discrete surface breathers in two-dimensional lattices of inductively coupled split-ring resonators with capacitive nonlinearity. We consider both conservative ͑Hamiltonian͒ and analyze the properties of the modes localized in space and periodic in time ͑discrete breathers͒ located in the corners and on the edges of the lattice. We find that surface breathers in the Hamiltonian systems have lower energy than their bulk counterparts and they are generally more stable.

We have studied properties of nonlinear waves in a mathematical model of a predator-prey system with pursuit and evasion. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially depends on the "taxis", represented by nonlinear "cross-diffusion" terms in the mathematical formulation. We have shown that the dependence of the velocity of wave propagation on the taxis has two distinct forms, "parabolic" and "linear". Transition from one form to the other correlates with changes in the shape of the wave profile. Dependence of the propagation velocity on diffusion in this system differs from the square-root dependence typical of reaction-diffusion waves. We demonstrate also that, for systems with negative and positive taxis, for example, pursuit and evasion, there typically exists a large region in the parameter space, where the waves demonstrate quasisoliton interaction: colliding waves can penetrate through each other, and waves can also reflect from impermeable boundaries.