The Hirota's bilinear method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Kadomtsev-Petviashvili equation

Abstract In this work we derive a new completely integrable dispersive equation. The equation is obtained by combining the Sawada–Kotera (SK) equation with the sense of the Kadomtsev–Petviashvili (KP) equation. The newly derived Sawada–Kotera–Kadomtsev–Petviashvili (SK–KP) equation is studied by using the tanh–coth method, to obtain single-soliton solution, and by the Hirota bilinear method, to determine the N -soliton solutions. The study highlights the significant features of the employed methods and its capability of handling completely integrable equations.

[1]  W. Hereman,et al.  The tanh method: I. Exact solutions of nonlinear evolution and wave equations , 1996 .

[2]  広田 良吾,et al.  The direct method in soliton theory , 2004 .

[3]  Abdul-Majid Wazwaz,et al.  Partial differential equations : methods and applications , 2002 .

[4]  W. Malfliet,et al.  The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations , 2004 .

[5]  S. Sawada,et al.  A Method for Finding N-Soliton Solutions of the KdV and KdV-Like Equation , 1974 .

[6]  Abdul-Majid Wazwaz,et al.  The tanh–coth and the sech methods for exact solutions of the Jaulent–Miodek equation , 2007 .

[7]  Abdul-Majid Wazwaz,et al.  Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method , 2007, Appl. Math. Comput..

[8]  Abdul-Majid Wazwaz,et al.  The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations , 2007, Appl. Math. Comput..

[9]  R. Hirota.  Exact solution of the Korteweg-deVries equation for multiple collision of solitons , 1971 .

[10]  Abdul-Majid Wazwaz,et al.  The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations , 2007, Appl. Math. Comput..

[11]  Ryogo Hirota,et al.  A New Form of Bäcklund Transformations and Its Relation to the Inverse Scattering Problem , 1974 .

[12]  Ryogo Hirota,et al.  Exact Solution of the Modified Korteweg-de Vries Equation for Multiple Collisions of Solitons , 1972 .

[13]  Abdul-Majid Wazwaz,et al.  Multiple-front solutions for the Burgers equation and the coupled Burgers equations , 2007, Appl. Math. Comput..

[14]  Ryogo Hirota,et al.  Exact Solution of the Sine-Gordon Equation for Multiple Collisions of Solitons , 1972 .

[15]  Jarmo Hietarinta,et al.  A Search for Bilinear Equations Passing Hirota''s Three-Soliton Condition , 1987 .

[16]  W. Hereman,et al.  The tanh method: II. Perturbation technique for conservative systems , 1996 .

[17]  Yoshimasa Matsuno,et al.  Bilinear Transformation Method , 1984 .

[18]  W. Hereman,et al.  Symbolic Software for Soliton Theory , 1995 .

[19]  Willy Hereman,et al.  Symbolic methods to construct exact solutions of nonlinear partial differential equations , 1997 .

[20]  J. Weiss,et al.  On classes of integrable systems and the Painlevé property , 1984 .

[21]  Abdul-Majid Wazwaz,et al.  New solitary-wave special solutions with compact support for the nonlinear dispersive K(m, n) equations , 2002 .

[22]  Abdul-Majid Wazwaz,et al.  The tanh method for traveling wave solutions of nonlinear equations , 2004, Appl. Math. Comput..

[23]  Alfred Ramani,et al.  The Miura transformations of Kaup's equation and of Mikhailov's equation , 1980 .

[24]  W. Malfliet.  Solitary wave solutions of nonlinear wave equations , 1992 .

[25]  Willy Hereman,et al.  Symbolic Computation of Conserved Densities for Systems of Nonlinear Evolution Equations , 1997, J. Symb. Comput..