Rational solutions for a (2+1)-dimensional nonlinear model in water waves generated by the Jaulent-Miodek hierarchy

被引：2

作者：

Yang, Jin-Wei

Gao, Yi-Tian ^{[1
]}

Su, Chuan-Qi

Zhao, Chen

Feng, Yu-Jie

机构：

[1] Beijing Univ Aeronaut & Astronaut, Minist Educ, Key Lab Fluid Mech, Beijing 100191, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2016年 / 72卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Nonlinear water waves; Nonlinear evolution equation; Jaulent-Miodek hierarchy; Rational solutions; Hirota's bilinear method; Pfaffian; BILINEAR BACKLUND-TRANSFORMATIONS; N-SOLITON SOLUTION; SCHRODINGER-EQUATION; EVOLUTION EQUATION; ROGUE WAVES; COLLISIONS; DYNAMICS;

D O I：

10.1016/j.camwa.2016.08.023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with a (2+1)-dimensional nonlinear evolution equation (NLEE) generated by the Jaulent-Miodek hierarchy for nonlinear water waves via the Hirota's bilinear method and Pfaffian. First, we construct rational solutions for general bilinear equations, and then convert the target bilinear equations to the general ones to obtain their rational solutions. The Pfaffian plays a role to simplifying the computations compared with the determinant way in the existing literatures. Once the first-and second-order rational solutions have been obtained, the higher-order solutions can be derived by the same token. Figures for the first-and second-order rational solutions are plotted and analyzed. As an application, the rational solutions for the modified Kadomtsev-Petviashvili equation have also been constructed. The method might be used for some other NLEEs to construct their rational solutions. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：2685 / 2693

页数：9

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