New exact solutions to the (2+1)-dimensional Ito equation: Extended homoclinic test technique

被引：25

作者：

Li, Dong-Long ^{[2
]}

Zhao, Jun-Xiao ^{[1
,3
]}

机构：

[1] Inst Appl Phys & Computat Math, Beijing 100000, Peoples R China

[2] Guangxi Univ Technol, Liuzhou 545006, Peoples R China

[3] Chinese Acad Sci, Grad Univ, Sch Math Sci, Beijing 100049, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 215卷 / 05期

关键词：

The (2+1)-dimensional Ito equation; Hirota bilinear method; Extended homoclinic test; Solitary wave; Periodic wave; Periodic solitary wave; SHALLOW-WATER WAVES; N-SOLITON SOLUTIONS; NONLINEAR EVOLUTION;

D O I：

10.1016/j.amc.2009.07.058

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Exact soliton solutions to the (2 + 1)-dimensional Ito equation are studied based on the idea of extended homoclinic test and bilinear method. Some explicit solutions, such as triangle function solutions, soliton solutions, doubly-periodic wave solutions and periodic solitary wave solutions, are obtained. It shows that the (2 + 1)-dimensional Ito equation has richer solutions. Besides, the elastic interactions of the solutions and their corresponding physical meaning are discussed. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：1968 / 1974

页数：7

共 22 条

[1] On the numerical solution of the sine-Gordon equation .1. Integrable discretizations and homoclinic manifolds [J].

Ablowitz, MJ ;

Herbst, BM ;

Schober, C .

JOURNAL OF COMPUTATIONAL PHYSICS, 1996, 126 (02) :299-314

[2]

ABLOWITZ MJ, 1974, STUD APPL MATH, V53, P249

[3]

[Anonymous], COMPUT APPL MATH 2

[4]

[Anonymous], 1980, SOLITONS

[5] Exact cross kink-wave solutions and resonance for the Jimbo-Miwa equation [J].

Dai, Zhengde ;

Li, Zitian ;

Liu, Zhenjiang ;

Li, Donglong .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2007, 384 (02) :285-290

[6] N-SOLITON SOLUTIONS OF MODEL EQUATIONS FOR SHALLOW-WATER WAVES [J].

HIROTA, R ;

SATSUMA, J .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1976, 40 (02) :611-612

[7]

Hirota R., 1976, Progress of Theoretical Physics Supplement, P64, DOI 10.1143/PTPS.59.64

[8] EXACT SOLUTION OF KORTEWEG-DE VRIES EQUATION FOR MULTIPLE COLLISIONS OF SOLITONS [J].

HIROTA, R .

PHYSICAL REVIEW LETTERS, 1971, 27 (18) :1192-+

[9]

Hirota R., 2004, The Direct Method in Soliton Theory

[10] NONLINEAR SUPERPOSITION FORMULAS OF THE ITO EQUATION AND A MODEL EQUATION FOR SHALLOW-WATER WAVES [J].

HU, XB ;

LI, Y .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1991, 24 (09) :1979-1986

← 1 2 3 →