Bifurcation and exact travelling wave solutions for Gardner-KP equation

By using the bifurcation theory of dynamical systems, this paper researches the bifurcation and exact travelling wave solutions for Gardner-KP equation. As a result, exact parametric representations of all wave solutions, including solitary wave solution, periodic wave solution, kink (anti-kink) wave solution and breaking wave solution, are given.

[1]  Abdul-Majid Wazwaz,et al.  Solitons and singular solitons for the Gardner-KP equation , 2008, Appl. Math. Comput..

[2]  Abdul-Majid Wazwaz,et al.  Sub-ODE method and soliton solutions for the variable-coefficient mKdV equation , 2009, Appl. Math. Comput..

[3]  Abdul-Majid Wazwaz,et al.  New solitons and kink solutions for the Gardner equation , 2007 .

[4]  B. Konopelchenko Inverse spectral transform for the (2 + 1)-dimensional Gardner equation , 1991 .

[5]  Guanrong Chen,et al.  Bifurcations of Traveling Wave Solutions for Four Classes of Nonlinear Wave Equations , 2005, Int. J. Bifurc. Chaos.

[6]  A. Degasperis A modified Korteweg-de Vries equation , 1987 .

[7]  Jie-Fang Zhang,et al.  New Solitary Wave Solution of the Combined KdV and mKdV Equation , 1998 .

[8]  Mark W. Coffey,et al.  On series expansions giving closed-form solutions of Korteweg-de Vries-like equations , 1990 .

[9]  Haihong Liu,et al.  The Exact Traveling wave solutions and their bifurcations in the Gardner and Gardner-KP equations , 2012, Int. J. Bifurc. Chaos.

[10]  C. S. Gardner,et al.  Method for solving the Korteweg-deVries equation , 1967 .

[11]  Mohd Nor Mohamad,et al.  Exact solutions to the combined KdV and mKdV equation , 1992 .

[12]  M. Wadati,et al.  Wave Propagation in Nonlinear Lattice. III , 1975 .

[13]  D. Korteweg,et al.  XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves , 1895 .

[14]  B. Kadomtsev,et al.  On the Stability of Solitary Waves in Weakly Dispersing Media , 1970 .