Papers by Sakkaravarthi K
The exact bright one-and two-soliton solutions of a particular type of coherently coupled nonline... more The exact bright one-and two-soliton solutions of a particular type of coherently coupled nonlinear Schrödinger equations, with alternate signs of nonlinearities among the two components, are obtained using the non-standard Hirota's bilinearization method. We find that in contrary to the coherently coupled nonlinear Schrödinger equations with same signs of nonlinearities the present system supports only coherently coupled solitons arising due to an interplay between dispersion and the nonlinear effects, namely, self-phase modulation, cross-phase modulation, and four-wave mixing process, thereby depend on the phases of the two co-propagating fields. The other type of soliton, namely, incoherently coupled solitons which are insensitive to the phases of the co-propagating fields and arise in a similar kind of coherently coupled nonlinear Schrödinger equations but with same signs of nonlinearities are not at all possible in the present system. The present system can support regular solution for the choice of soliton parameters for which mixed coupled nonlinear Schrödinger equations admit only singular solution. Our analysis on the collision dynamics of the bright solitons reveals the important fact that in contrary to the other types of coupled nonlinear Schrödinger systems the bright solitons of the present system can undergo only elastic collision in spite of their multicomponent nature. We also show that regular two-soliton bound states can exist even for the choice for which the same system admits singular one-soliton solution. Another important effect identified regarding the bound solitons is that the breathing effects of these bound solitons can be controlled by tuning the additional soliton parameters resulting due to the multicom-ponent nature of the system which do not have any significant effects on bright one soliton propagation and also in soliton collision dynamics. C 2013 American Institute of Physics.[http://dx.doi.org/10.1063/1.4772611]
The soliton solutions of an integrable three component Gross-Pitaevskii equations, governing the ... more The soliton solutions of an integrable three component Gross-Pitaevskii equations, governing the dynamics of F = 1 spinor Bose-Einstein condensates are obtained by using a non-standard type of Hirota's bilinearization method and the solitons are classified as polar and ferromagnetic solitons based on the presence or absence of spin-mixing nonlinearities. The present system exhibits different types of soliton profiles such as single-hump, double-hump and flat-top solitons. The interesting soliton collisions are also studied.
We consider the integrable two-component coherently coupled nonlinear Schrödinger equation, with ... more We consider the integrable two-component coherently coupled nonlinear Schrödinger equation, with a relative sign change between the coefficients of four wave mixing term and the self-phase as well as cross-phase modulation terms. By applying a non-standard type of Hirota's bilinearization technique, we obtain novel bright solitons which admit double hump profile in general. However the standard single hump solitons result for specific choices. We discuss the fascinating collision dynamics of the double hump soliton with a single hump soliton. Also, we analyse the collision behaviour of double hump solitons and that of single hump solitons, separately.
We construct the dark one-and two-soliton solutions of a multi-component Yajima-Oikawa system by ... more We construct the dark one-and two-soliton solutions of a multi-component Yajima-Oikawa system by using the Hirota's bilinear method. We have investigated their propagation and collision dynamics. Especially, we have revealed the role of the nonlinearity coefficients on the soliton dynamics in the multicomponent Yajima-Oikawa system.
We have obtained the bright one-and two-soliton solutions of the two-component general-coupled no... more We have obtained the bright one-and two-soliton solutions of the two-component general-coupled nonlinear Schrödinger equations by using the Hirota's bilinearization method. By studying the collision dynamics, we have pointed out that these two component bright solitons undergo interesting shape changing collision behaviour characterized by the energy redistribution and amplitude dependent phase-shifts which is not possible in their single component counterpart.
In this paper, we have studied the integrability nature of a system of three-coupled Gross–Pitaev... more In this paper, we have studied the integrability nature of a system of three-coupled Gross–Pitaevskii type nonlinear evolution equations arising in the context of spinor Bose–Einstein condensates by applying the Painlevé singularity structure analysis. We show that only for two sets of parametric choices, corresponding to the known integrable cases, the system passes the Painlevé test.
Bright plane soliton solutions of an integrable (2+1)-dimensional (n + 1)-wave system are obtaine... more Bright plane soliton solutions of an integrable (2+1)-dimensional (n + 1)-wave system are obtained by applying Hirota's bilinearization method. First, the soliton solutions of a three-wave system consisting of two shortwave components and one long-wave component are found and then the results are generalized to the corresponding integrable (n + 1)-wave system with n short waves and a single long wave. It is shown that the solitons in the shortwave components (say S (1) and S (2)) can be amplified by merely reducing the pulse width of the long-wave component (say L). Study of the collision dynamics reveals some interesting behaviour: the solitons which split up in the shortwave components undergo shape changing collisions with intensity redistribution and amplitude-dependent phase shifts. Even though a similar type of collision is possible in (1+1)-dimensional multicomponent integrable systems, to our knowledge we report this kind of collision in (2+1) dimensions for the first time. However, solitons which appear in the long-wave component exhibit only elastic collision though they undergo amplitude-dependent phase shifts.
In this paper, we discuss the fascinating energy sharing collisions of multicompo-nent solitons i... more In this paper, we discuss the fascinating energy sharing collisions of multicompo-nent solitons in certain incoherently coupled and coherently coupled nonlinear Schrödinger-type equations arising in the context of nonlinear optics.
It is well known that solitons in integrable systems recover their original profiles after their ... more It is well known that solitons in integrable systems recover their original profiles after their mutual collisions. This is not true in the case of optical fibre arrays, governed by a set of integrable coupled nonlinear Schrödinger (CNLS) equations. We consider the Manakov-and mixed-type 'two-component' CNLS systems. The most important characteristics of these systems are: (1) The polarizations of the two-component solitons are changed through their mutual collisions (Manakov system) and (2) the energy (intensity) switching occurs through the head-on collision (mixed system). By placing the above solitons on the primary star graph (PSG), we see that soliton collisions give rise to interesting phase changes in PSG: (a) The transition in PSG from its depolar-ized state to polarized one; (b) a state with selectively amplified bond is generated on PSG from its homogeneous state. These results will be applicable to network protocols using optical fibre arrays.
In this paper, we study the formation of solitons, their propagation and collision behaviour in a... more In this paper, we study the formation of solitons, their propagation and collision behaviour in an integrable multicomponent (2+1)-dimensional long wave–short wave resonance interaction (M-LSRI) system. First, we briefly revisit the earlier results on the dynamics of bright solitons and demonstrate the fascinating energy exchange collision of bright solitons appearing in the short-wave components of the M-LSRI system. Then, we explicitly construct the exact one-and two-multicomponent dark soliton solutions of the M-LSRI system by using the Hirota’s direct method and explore its propagation dynamics. Also, we study the features of dark soliton collisions.
We investigate the dynamics of bright matter wave solitons in spin-1 Bose–Einstein condensates wi... more We investigate the dynamics of bright matter wave solitons in spin-1 Bose–Einstein condensates with time modulated nonlinearities. We obtain soliton solutions of an integrable autonomous three-coupled Gross–Pitaevskii (3-GP) equations using Hirota's method involving a non-standard bilinearization. The similarity transformations are developed to construct the soliton solutions of non-autonomous 3-GP system. The non-autonomous solitons admit different density profiles. An interesting phenomenon of soliton compression is identified for kink-like nonlinearity coefficient with Hermite–Gaussian-like potential strength. Our study shows that these non-autonomous solitons undergo non-trivial collisions involving condensate switching.
We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO syste... more We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilin-earization method and explicitly analyze the one-and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave–short-wave resonance takes place. The shortwave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions—(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components—result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of shortwave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pairwise nature of collisions and unravel the fascinating state restoration property.
We consider the integrable multicomponent coherently coupled nonlinear Schrödinger (CCNLS) equati... more We consider the integrable multicomponent coherently coupled nonlinear Schrödinger (CCNLS) equations describing simultaneous propagation of multiple fields in Kerr-type nonlinear media. The correct bilinear equations of m-CCNLS equations are obtained using a non-standard type of Hirota's bilinearization method, and the more general bright one solitons with single-hump and double-hump profiles including special flat-top profiles are obtained. The solitons are classified as coherently coupled solitons and incoherently coupled solitons depending upon the presence and absence of coherent nonlinearity arising due to the existence of the co-propagating modes/components. Further, the more general two-soliton solutions are obtained using this non-standard bilinearization approach, and various fascinating collision dynamics are pointed out. Particularly, we demonstrate that the collision between coherently coupled solitons and incoherently coupled solitons displays a non-trivial behaviour in which the former always undergoes energy switching accompanied by an amplitude-dependent phase-shift and change in the relative separation distance, leaving the latter unaltered. But the collision between coherently coupled solitons alone is found to be a standard elastic collision. Our study also reveals the important fact that the collision between incoherently coupled solitons arising in the m-CCNLS system with m = 2 is always elastic, whereas for m > 2 the collision becomes intricate, and for this case the m-CCNLS system exhibits interesting energy-sharing collision of solitons characterized by intensity redistribution, amplitude-dependent phase-shift and change in relative separation distance, which is similar to that of the multicomponent Manakov soliton collisions. This suggests that the m-CCNLS system can also be a suitable candidate for soliton collision-based optical computing in addition to the Manakov system.
In this paper, we construct the bright-soliton bound states of an integrable (2+1)-dimensional mu... more In this paper, we construct the bright-soliton bound states of an integrable (2+1)-dimensional multicomponent long wave-short wave resonance interaction (LSRI) system by using the exact bright-soliton solutions obtained in Ref. [24] and analyze their interesting collision dynamics. We show that the beating and breathing oscillations of the bound solitons can be controlled by tuning the polarization parameters. Also, we explore the interaction between the bound-soliton and a standard soliton. We also point out that the two bound-soliton state seems to be robust against collision with a standard soliton and remain to be bounded even after collision.
We consider a general multicomponent (2+1)-dimensional long-wave–short-wave resonance interaction... more We consider a general multicomponent (2+1)-dimensional long-wave–short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlevé analysis. Then we construct the exact bright multisoliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one-and two-soliton solutions and studied their dynamics briefly.
Thesis Chapters by Sakkaravarthi K
Bharathidasan University, India: Ph.D. Thesis, 2015
Solitons are very important nonlinear entities in the recent years which find multifaceted applic... more Solitons are very important nonlinear entities in the recent years which find multifaceted applications in different branches of science, engineering, and technology, due to their ability to propagate over extraordinary distances without any loss of energy and remarkable stability under collisions. These solitons give rise to several interesting features in the associated nonlinear dynamical systems. Especially, the multicomponent solitons show distinct propagation characteristics and posses fascinating energy sharing collisions which are not possible in scalar (single component) solitons. In this thesis, we consider a set of multicomponent nonlinear dynamical systems, such as multicomponent Yajima-Oikawa equations in (1+1)-dimension, long-wave– short-wave resonance interaction equations in (2+1)-dimensions, coherently coupled nonlinear Schro ̈dinger equations in the presence of four-wave mixing nonlinearities (with same type as well as opposite signs for nonlinearities), and three-coupled Gross-Pitaevskii equations with spin-mixing nonlinearities, arising in the context of nonlinear optics and Bose-Einstein condensates. After studying the integrability nature of these equations, we construct explicit multicomponent soliton solutions which supports a variety of profiles like single-hump, double-hump, flat-top, dark (hole), and gray solitons for different choices of parameters. Our studies on bright soliton collisions reveal different types of energy-sharing and energy-switching collisions in addition to their elastic collisions. Studies on special solutions like bound states and resonant solitons show periodic oscillations which can be controlled by altering the polarization parameters. But, the dark solitons admit only elastic collisions. Our results can find interesting applications in different context of nonlinear science.
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Papers by Sakkaravarthi K
Thesis Chapters by Sakkaravarthi K