On integrability and quasi-periodic wave solutions to a (3+1)-dimensional generalized KdV-like model equation

被引:84
作者
Wang, Xiu-Bin [1 ,2 ]
Tian, Shou-Fu [1 ,2 ,3 ]
Xua, Mei-Juan [1 ,2 ]
Zhang, Tian-Tian [1 ,2 ]
机构
[1] China Univ Min & Technol, Dept Math, Xuzhou 221116, Peoples R China
[2] China Univ Min & Technol, Ctr Nonlinear Equat, Xuzhou 221116, Peoples R China
[3] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 0WA, England
关键词
A (3+1)-dimensional generalized KdV-like model equation; Bell polynomial; Backlund transformation; Lax pairs; Soliton solution; Periodic wave solution; KADOMTSEV-PETVIASHVILI EQUATION; RATIONAL CHARACTERISTICS; SOLITON-SOLUTIONS; LIE SYMMETRIES; EVOLUTION; TRANSFORMATIONS; SYSTEMS; LAW;
D O I
10.1016/j.amc.2016.02.028
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Under investigation in this paper is the integrability of a (3+1)-dimensional generalized KdV-like model equation, which can be reduced to several integrable equations. With help of Bell polynomials, an effective method is presented to succinctly derive the bilinear formalism of the equation, based on which, the soliton solutions and periodic wave solutions are also constructed by using Riemann theta function. Furthermore, the Backlund transformation, Lax pairs, and infinite conservation laws of the equation can easily be derived, respectively. Finally, the relationship between periodic wave solutions and soliton solutions are systematically established. It is straightforward to verify that these periodic waves tend to soliton solutions under a small amplitude limit. (c) 2016 ElsevierInc. Allrightsreserved.
引用
收藏
页码:216 / 233
页数:18
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