Explicit bi-soliton-like solutions for a generalized KP equation with variable coefficients

A generalized KP equation with variable coefficients, including the KP equation and the cylindrical KP equation as its special cases is investigated using a constructive algorithm and symbolic computation. Explicit bi-soliton-like solutions of the equation are obtained under certain constraints on the coefficient functions. For different coefficient functions, the solutions can model different types of bi-soliton-like waves. Some interesting bi-soliton-like waves are graphically revealed.

[1]  Heng-Nong Xuan,et al.  Families of non-travelling wave solutions to a generalized variable coefficient two-dimensional KdV equation using symbolic computation , 2004 .

[2]  Anjan Biswas,et al.  1-Soliton solution of Kadomtsev-Petviashvili equation with power law nonlinearity , 2009, Appl. Math. Comput..

[3]  Hon-Wah Tam,et al.  Grammian solutions and pfaffianization of a non-isospectral and variable-coefficient Kadomtsev–Petviashvili equation , 2008 .

[4]  Bo Tian,et al.  Spherical Kadomtsev-Petviashvili equation and nebulons for dust ion-acoustic waves with symbolic computation , 2005 .

[5]  Zhenya Yan,et al.  Bäcklund transformation, non-local symmetry and exact solutions for (2+1)-dimensional variable coefficient generalized KP equations , 2000 .

[6]  R. S. Johnson.  Water waves and Korteweg–de Vries equations , 1980, Journal of Fluid Mechanics.

[7]  Bo Tian,et al.  Cylindrical Kadomtsev–Petviashvili model, nebulons and symbolic computation for cosmic dust ion-acoustic waves , 2006 .

[8]  Zhang Yi,et al.  Grammian Solutions to a Variable-Coefficient KP Equation , 2008 .

[9]  Emmanuel Yomba,et al.  Construction of new soliton-like solutions for the (2 + 1) dimensional KdV equation with variable coefficients , 2004 .

[10]  P. Clarkson,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering: References , 1991 .

[11]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[12]  Anjan Biswas,et al.  Solitary wave solution for KdV equation with power-law nonlinearity and time-dependent coefficients , 2009 .

[13]  Xiaonan Li,et al.  Painlevé analysis and new analytic solutions for variable-coefficient Kadomtsev-Petviashvili equation with symbolic computation , 2010, Appl. Math. Comput..

[14]  Bo Tian,et al.  Truncated Painlevé expansion and a wide-ranging type of generalized variable-coefficient Kadomtsev-Petviashvili equations , 1995 .

[15]  Zhu Hong-Wu,et al.  Wronskian and Grammian Determinant Solutions for a Variable-Coefficient Kadomtsev–Petviashvili Equation , 2008 .

[16]  S. A. El-Wakil,et al.  New exact solutions for a generalized variable coefficients 2D KdV equation , 2004 .