Solitary waves, homoclinic breather waves and rogue waves of the (3+1)-dimensional Hirota bilinear equation

被引：108

作者：

Dong, Min-Jie ^{[1
,2
]}

Tian, Shou-Fu ^{[1
,2
]}

Yan, Xue-Wei ^{[1
,2
]}

Zou, Li ^{[3
,4
]}

机构：

[1] China Univ Min & Technol, Sch Math, Xuzhou 221116, Peoples R China

[2] China Univ Min & Technol, Inst Math Phys, Xuzhou 221116, Peoples R China

[3] Dalian Univ Technol, Sch Naval Architecture, State Key Lab Struct Anal Ind Equipment, Dalian 116024, Peoples R China

[4] Collaborat Innovat Ctr Adv Ship & Deep Sea Explor, Shanghai 200240, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2018年 / 75卷 / 03期

关键词：

The (3+1)-dimensional Hirota bilinear equation; Bilinear form; Solitary waves; Rogue waves; Homoclinic breather waves; KADOMTSEV-PETVIASHVILI EQUATION; NONLINEAR SCHRODINGER-EQUATION; (2+1)-DIMENSIONAL BOUSSINESQ EQUATION; RATIONAL CHARACTERISTICS; GEOMETRIC APPROACH; CONSERVATION-LAWS; FLUID-DYNAMICS; LIE SYMMETRIES; ITO EQUATION; INTEGRABILITY;

D O I：

10.1016/j.camwa.2017.10.037

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the (3 + 1)-dimensional Hirota bilinear equation is investigated, which can be used to describe the nonlinear dynamic behavior in physics. By using the Bell polynomials, the bilinear form of the equation is derived in a very natural way. Based on the resulting bilinear form, its N-solitary waves are further obtained by using the Hi rota's bilinear theory. Finally, by using the Homoclinic test method, we obtain its rational breather wave and rogue wave solutions, respectively. In order to better understand the dynamical behaviors of the equation, some graphical analyses are discussed for these exact solutions. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：957 / 964

页数：8

共 58 条

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