The extended tanh method is used to derive new solitons solutions for several forms of the fifth-... more The extended tanh method is used to derive new solitons solutions for several forms of the fifth-order nonlinear KdV equation. The forms include the Lax, Sawada-Kotera (SK), Sawada-Kotera-Parker-Dye (SKPD), Kaup-Kupershmidt (KK), Kaup-Kupershmidt-Parker-Dye (KKPD), and the Ito equations. The criteria established in [A.M. Wazwaz, Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.02.047] to build up reliable relations between the parameters of the equation are confirmed by using this new approach. Entirely new bell shaped solitons are determined.
In this work, multiple-front solutions for the Burgers equation and the coupled Burgers equations... more In this work, multiple-front solutions for the Burgers equation and the coupled Burgers equations are examined. The tanh-coth method and the Cole-Hopf transformation are used. The work highlights the power of the proposed schemes and the structures of the obtained multiple-front solutions.
In this paper, we present a computational approach to develop soliton solutions of the nonlinear ... more In this paper, we present a computational approach to develop soliton solutions of the nonlinear Kadomtsev±Petviashvili equation. Our approach rests mainly on the Adomian decomposition method to include few components of the decomposition series. The proposed framework is presented in a general way so that it can be used in nonlinear evolution equations of the same type. Numerical examples are tested to illustrate the proposed scheme. Ó
Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment, 2004
For 17 days in August and September 2002, the LIGO and GEO interferometer gravitational wave dete... more For 17 days in August and September 2002, the LIGO and GEO interferometer gravitational wave detectors were operated in coincidence to produce their first data for scientific analysis. Although the detectors were still far from their design sensitivity levels, the data can be used to place better upper limits on the flux of gravitational waves incident on the earth than previous direct measurements. This paper describes the instruments and the data in some detail, as a companion to analysis papers based on the first data.
In this paper we study nonlinear variants of the KdV and the KP equations with positive and negat... more In this paper we study nonlinear variants of the KdV and the KP equations with positive and negative exponents. The sine–cosine algorithm is employed to back up the proposed analysis. The work reveals new exact solutions with compactons, solitons, solitary patterns ...
In this work, we will compare the performance of the Adomian decomposition method and the Taylor ... more In this work, we will compare the performance of the Adomian decomposition method and the Taylor series method applied to the solution of linear and nonlinear ordinary differential equations. The comparison shows that the decomposition method is reliable, efficient and easy to use from a computational viewpoint. Although the two methods provide the solution in an infinite series, the decomposition method provides a fast convergent series of easily computable components and eliminates cumbersome computational work needed by Taylor series method.
In this work, systems of linear and nonlinear partial dierential equations and the reaction±diusi... more In this work, systems of linear and nonlinear partial dierential equations and the reaction±diusion Brusselator model are handled by applying the decomposition method. The advantage of this work is twofold. Firstly, the decomposition method reduces the computational work. Secondly, in comparison with existing techniques, the decomposition method is an improvement with regard to its accuracy and rapid convergence. The decomposition method has the advantage of being more concise for analytical and numerical purposes. Ó
In this paper, a reliable algorithm is employed to investigate the dierential equations of Lane±E... more In this paper, a reliable algorithm is employed to investigate the dierential equations of Lane±Emden type. The algorithm rests mainly on the Adomian decomposition method with an alternate framework designed to overcome the diculty of the singular point. The proposed framework is applied to a generalization of Lane±Emden equations so that it can be used in dierential equations of the same type. Ó (A.-M. Wazwaz).
It is well-known that the nonlinear term uu x in the KdV equation causes the steepening of wave f... more It is well-known that the nonlinear term uu x in the KdV equation causes the steepening of wave form. However, the dispersion effect term u xxx in the same equation makes the wave form spread [1]. Due to the balance between this weak nonlinearity and dispersion, solitons exist. ...
The nonlinear Klein-Gordon equation is used as a vehicle to employ the tanh method and the sine-c... more The nonlinear Klein-Gordon equation is used as a vehicle to employ the tanh method and the sine-cosine method to formally derive a number of travelling wave solutions. The study features a variety of solutions with distinct physical structures. The work shows that one method complements the other, and each method gives solutions of formal properties. The obtained solutions include compactons, solitons, solitary patterns, and periodic solutions.
Kami telah mengaudit neraca PT ETSA pada tanggal 31 Desember 2007 dan 2006, laporan laba rugi, la... more Kami telah mengaudit neraca PT ETSA pada tanggal 31 Desember 2007 dan 2006, laporan laba rugi, laporan perubahan ekuitas, dan laporan arus kas untuk tahun yang berakhir pada tanggal-tanggal tersebut. Laporan keuangan adalah tanggung jawab manajemen perusahaan.
The extended tanh method is used to derive new solitons solutions for several forms of the fifth-... more The extended tanh method is used to derive new solitons solutions for several forms of the fifth-order nonlinear KdV equation. The forms include the Lax, Sawada-Kotera (SK), Sawada-Kotera-Parker-Dye (SKPD), Kaup-Kupershmidt (KK), Kaup-Kupershmidt-Parker-Dye (KKPD), and the Ito equations. The criteria established in [A.M. Wazwaz, Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.02.047] to build up reliable relations between the parameters of the equation are confirmed by using this new approach. Entirely new bell shaped solitons are determined.
In this work, multiple-front solutions for the Burgers equation and the coupled Burgers equations... more In this work, multiple-front solutions for the Burgers equation and the coupled Burgers equations are examined. The tanh-coth method and the Cole-Hopf transformation are used. The work highlights the power of the proposed schemes and the structures of the obtained multiple-front solutions.
In this paper, we present a computational approach to develop soliton solutions of the nonlinear ... more In this paper, we present a computational approach to develop soliton solutions of the nonlinear Kadomtsev±Petviashvili equation. Our approach rests mainly on the Adomian decomposition method to include few components of the decomposition series. The proposed framework is presented in a general way so that it can be used in nonlinear evolution equations of the same type. Numerical examples are tested to illustrate the proposed scheme. Ó
Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment, 2004
For 17 days in August and September 2002, the LIGO and GEO interferometer gravitational wave dete... more For 17 days in August and September 2002, the LIGO and GEO interferometer gravitational wave detectors were operated in coincidence to produce their first data for scientific analysis. Although the detectors were still far from their design sensitivity levels, the data can be used to place better upper limits on the flux of gravitational waves incident on the earth than previous direct measurements. This paper describes the instruments and the data in some detail, as a companion to analysis papers based on the first data.
In this paper we study nonlinear variants of the KdV and the KP equations with positive and negat... more In this paper we study nonlinear variants of the KdV and the KP equations with positive and negative exponents. The sine–cosine algorithm is employed to back up the proposed analysis. The work reveals new exact solutions with compactons, solitons, solitary patterns ...
In this work, we will compare the performance of the Adomian decomposition method and the Taylor ... more In this work, we will compare the performance of the Adomian decomposition method and the Taylor series method applied to the solution of linear and nonlinear ordinary differential equations. The comparison shows that the decomposition method is reliable, efficient and easy to use from a computational viewpoint. Although the two methods provide the solution in an infinite series, the decomposition method provides a fast convergent series of easily computable components and eliminates cumbersome computational work needed by Taylor series method.
In this work, systems of linear and nonlinear partial dierential equations and the reaction±diusi... more In this work, systems of linear and nonlinear partial dierential equations and the reaction±diusion Brusselator model are handled by applying the decomposition method. The advantage of this work is twofold. Firstly, the decomposition method reduces the computational work. Secondly, in comparison with existing techniques, the decomposition method is an improvement with regard to its accuracy and rapid convergence. The decomposition method has the advantage of being more concise for analytical and numerical purposes. Ó
In this paper, a reliable algorithm is employed to investigate the dierential equations of Lane±E... more In this paper, a reliable algorithm is employed to investigate the dierential equations of Lane±Emden type. The algorithm rests mainly on the Adomian decomposition method with an alternate framework designed to overcome the diculty of the singular point. The proposed framework is applied to a generalization of Lane±Emden equations so that it can be used in dierential equations of the same type. Ó (A.-M. Wazwaz).
It is well-known that the nonlinear term uu x in the KdV equation causes the steepening of wave f... more It is well-known that the nonlinear term uu x in the KdV equation causes the steepening of wave form. However, the dispersion effect term u xxx in the same equation makes the wave form spread [1]. Due to the balance between this weak nonlinearity and dispersion, solitons exist. ...
The nonlinear Klein-Gordon equation is used as a vehicle to employ the tanh method and the sine-c... more The nonlinear Klein-Gordon equation is used as a vehicle to employ the tanh method and the sine-cosine method to formally derive a number of travelling wave solutions. The study features a variety of solutions with distinct physical structures. The work shows that one method complements the other, and each method gives solutions of formal properties. The obtained solutions include compactons, solitons, solitary patterns, and periodic solutions.
Kami telah mengaudit neraca PT ETSA pada tanggal 31 Desember 2007 dan 2006, laporan laba rugi, la... more Kami telah mengaudit neraca PT ETSA pada tanggal 31 Desember 2007 dan 2006, laporan laba rugi, laporan perubahan ekuitas, dan laporan arus kas untuk tahun yang berakhir pada tanggal-tanggal tersebut. Laporan keuangan adalah tanggung jawab manajemen perusahaan.
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