Variable separation solutions for the (3 + 1)-dimensional Jimbo-Miwa equation

Abstract Two types of variable separation solutions, obtained by the multi-linear variable separation approach, for the ( 3 + 1 ) -dimensional Jimbo–Miwa equation are presented in this Letter. Some two-dimensional arbitrary functions are included in the solutions which lead to some interesting ( 3 + 1 ) -dimensional structures.

[1]  S. Lou,et al.  Extended multilinear variable separation approach and multivalued localized excitations for some (2+1)-dimensional integrable systems , 2003 .

[2]  Ji Lin,et al.  The interactions of localized coherent structures for a (2 + 1)-dimensional system , 2003 .

[3]  Lou Sen-yue,et al.  Fractal Solutions of the Nizhnik-Novikov-Veselov Equation , 2002 .

[4]  Xi-Qiang Liu,et al.  New solutions of the 3 + 1 dimensional Jimbo-Miwa equation , 2004, Appl. Math. Comput..

[5]  Deformation and (3+1)-dimensional integrable model , 2000 .

[6]  Xiao-yan Tang,et al.  Variable separation solutions obtained from Darboux Transformations for the asymmetric Nizhnik–Novikov–Veselov system , 2004 .

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

[8]  C. Zheng,et al.  New variable separation excitations of (2 + 1)-dimensional dispersive long-water wave system obtained by an extended mapping approach☆ , 2005 .

[9]  Zhang Jie-Fang,et al.  Bäcklund transformation and multiple soliton solutions for the (3+1)-dimensional Jimbo-Miwa equation , 2002 .

[10]  Lou Sen-yue,et al.  Conditional Similarity Solutions of (2+1)-Dimensional General Nonintegrable KdV Equation , 2002 .

[11]  Generalized W∞ symmetry algebra of the conditionally integrable nonlinear evolution equation , 1995 .

[12]  Construction of the Darboux Transformaiton and Solutions to the Modified Nizhnik–Novikov–Veselov Equation , 2004 .

[13]  S. Lou,et al.  Special solutions from the variable separation approach: the Davey - Stewartson equation , 1996 .

[14]  P. Winternitz,et al.  Point symmetries of conditionally integrable nonlinear evolution equations , 1990 .

[15]  Lou Sen-yue.  Localized Excitations in (3+1) Dimensions: Dromions, Ring-Shape and Bubble-Like Solitons , 2004 .

[16]  Alfred Ramani,et al.  Are all the equations of the Kadomtsev–Petviashvili hierarchy integrable? , 1986 .

[17]  Bin Wu,et al.  Painlevé analysis and special solutions of generalized Broer-Kaup equations , 2002 .

[18]  Engui Fan,et al.  An algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinea , 2003 .

[19]  S. Lou,et al.  Localized excitations of the (2 + 1)-dimensional sine-Gordon system , 2003 .

[20]  Ma Hong-cai.  A Simple Method to Generate Lie Point Symmetry Groups of the (3+1)-Dimensional Jimbo?Miwa Equation , 2005 .

[21]  Lou Sen-yue,et al.  Multilinear Variable Separation Approach in (3+1)-Dimensions: the Burgers Equation , 2003 .

[22]  Ying Zhang,et al.  Localized excitations in (2+1)-dimensional systems. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.