Applied Mathematics and Computation

A set of sufficient conditions consisting of systems of linear partial differential equations is obtained which guarantees that the Wronskian determinant solves the (3 + 1)-dimensional Jimbo–Miwa equation in the bilinear form. Upon solving the linear conditions, the resulting Wronskian formulations bring solution formulas, which can yield rational solutions, solitons, negatons, positons and interaction solutions.

[1]  Yi Zhang,et al.  The exact solutions to the complex KdV equation , 2007 .

[2]  Wen-Xiu Ma,et al.  Complexiton solutions of the Toda lattice equation , 2004 .

[3]  Wen-Xiu Ma,et al.  Wronskian solutions to integrable equations , 2009 .

[4]  Wenxiu Ma,et al.  A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation , 2009, 0903.5337.

[5]  V. Matveev,et al.  Positon-positon and soliton-positon collisions: KdV case , 1992 .

[6]  Zhenya Yan.  Multiple solution profiles to the higher-dimensional Kadomtsev–Petviashvilli equations via Wronskian determinant , 2007 .

[7]  Wenxiu Ma.  Wronskians, generalized Wronskians and solutions to the Korteweg–de Vries equation , 2003, nlin/0303068.

[8]  Jianping Wu.  N-soliton solution, generalized double Wronskian determinant solution and rational solution for a (2+1)-dimensional nonlinear evolution equation , 2008 .

[9]  Abdul-Majid Wazwaz,et al.  Multiple-soliton solutions for the Calogero-Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF equations , 2008, Appl. Math. Comput..

[10]  Jie Ji,et al.  The double Wronskian solutions of a non-isospectral Kadomtsev–Petviashvili equation , 2008 .

[11]  Wen-Xiu Ma,et al.  Wronskian solutions of the Boussinesq equation—solitons, negatons, positons and complexitons , 2007 .

[12]  J. Nimmo,et al.  A method of obtaining the N-soliton solution of the Boussinesq equation in terms of a wronskian , 1983 .

[13]  J. Nimmo,et al.  Soliton solutions of the Korteweg-de Vries and Kadomtsev-Petviashvili equations: The wronskian technique , 1983 .

[14]  Wenxiu Ma,et al.  A second Wronskian formulation of the Boussinesq equation , 2009 .

[15]  E. Zayed,et al.  TRAVELING WAVE SOLUTIONS FOR HIGHER DIMENSIONAL NONLINEAR EVOLUTION EQUATIONS USING THE $(\frac{G'}{G})$- EXPANSION METHOD , 2010 .

[16]  M. Jimbo,et al.  Solitons and Infinite Dimensional Lie Algebras , 1983 .

[17]  Wenxiu Ma,et al.  Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions , 2004, nlin/0503001.

[18]  Xianguo Geng,et al.  N-soliton solution and its Wronskian form of a (3+1)-dimensional nonlinear evolution equation , 2007 .