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Exotic Localized Coherent Structures of the （2＋1）—Dimensional Dispersive Long—Wave Equation

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Communications in Theoretical Physics 2002年第3期37卷 277-282页

作者： ZHANGJie－Fang InstituteofNonlinearPhysics ZhejiangNormalUniversityJinhua321004China

This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous balance method, we find that the richness of the localized coherent structures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers, instantons and ring solitons.

关键词： extended homogeneous balance method coherent soliton structures dispersive long-wave equation the (2+1)-dimensions

On an Auto-Baecklund Transformation for (2+1)-Dimensional VariableCoefficient Generalized KP Equations and Exact Solutions

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Communications in Theoretical Physics 2005年第4期43卷 677-680页

作者： BAICheng-Jie BAICheng-Lin HANJi-Guang ZHAOHong CommunicationSchool ShandongNormalUniversityJinan250014China PhysicsScienceandInformationEngineeringSchool LiaochengUniversityLiaocheng252059China

By the application of the extended homogeneous balance method, we derive anauto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KPequations. Based on the BT, in which there are two ... 详细信息

关键词： extended homogeneous balance method (2+1)-dimensional variable coefficientgeneralized KP equation auto-Baecklund transformation exact solutions

Oscillating Solitons for （2＋1）-Dimensional Nonlinear Models

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Communications in Theoretical Physics 2007年第2期47卷 282-286页

作者： Naranmandula Tubuxin College of Physics and Electromechanics Inner Mongolia University for NationalitiesTongliao 028043China

Using extended homogeneous balance method and variable separation hypothesis, we found new variable separation solutions with three arbitrary functions of the （2＋1）-dimensional dispersive long-wave equations, Based on derived solutions, we revealed abundant oscillating solitons such as dromion, multi-dromion, solitoff, solitary waves, and so on, by selecting appropriate functions.

关键词： oscillating soliton (2+1)-dimensional system extended homogeneous balance method

Some Special Types of Solitary Wave Solutions for （3＋1）-Dimensional Jimbo-MiwaEquation

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Communications in Theoretical Physics 2004年第6期41卷 875-877页

作者： BAICheng-Lin ZHAOHong DepartmentofCommunicationEngineering LiaochengUniversityLiaocheng252059China

Using the extended homogeneous balance method, we find some special types of single solitary wave solution and new types of the multisoliton solutions of the (3+1)-dimensional Jimbo-Miwa equation.

关键词： (3+1)-dimensional Jimbo-Miwa equation extended homogeneous balance method soliton solutions

Traveling wave solutions for shallow water equations

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Journal of Ocean Engineering and Science 2017年第1期2卷 28-33页

作者： U.M.Abdelsalam Department of Mathematics Faculty of ScienceFayoum UniversityAl FayoumEgypt

An extended homogeneous balance method is suggested in this *** on computerized symbolic computation and the homogeneous balance method,new exact traveling wave solutions of nonlinear partial differential equations(PDEs)are *** shallow-water equations represent a simple yet realistic set of equations typically found in atmospheric or ocean modeling applications,we consider the exact solutions of the nonlinear generalized shallow water equation and the fourth order Boussinesq *** this method,with the aid of Mathematica,many new exact traveling wave solutions are successfully obtained.

关键词： extended homogeneous balance method Shallow water equation Boussinesq equation Traveling wave solutions

New localized excitations in a （2＋1）-dimensional Broer-Kaup system

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Chinese Physics B 2005年第2期14卷 285-292页

作者：白成林刘希强赵红 PhysicsScienceandInformationEngineeringSchool LiaochengUniversityLiaocheng252059China MathematicalScienceSchool LiaochengUniversityLiaocheng252059China

Starting with the extended homogeneous balance method and a variable separation approach, a general variable separation solution of the Broer-Kaup system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakon and fractal localized solutions,some new types of localized excitations, such as compacton and folded excitations, are obtained by introducing appropriate lower-dimensional piecewise smooth functions and multiple-valued functions, and some interesting novel features of these structures are revealed.

关键词： extended homogeneous balance method variable separation approach localized excitations (2+1)-dimensional Broer-Kaup system

New multi—soliton solutions and travelling wave solutions of the dispersive long—wave equations

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Chinese Physics B 2002年第6期11卷 533-536页

作者：张解放郭冠平等 InstituteofNonlinearPhysics ZhejiangNormalUniversityJinhua321004China CollegeofEducationScienceandTechnology ZhejiangNormalUniversityJinhua321004China

Using the extended homogeneous balance method, the (1+1)-dimensional dispersive Iong-wave equations have been solved. Starting from the homogeneous balance method, we have obtained a nonlinear transformation for simplifying a dispersive long-wave equation into a linear partial differential equation. Usually, we can obtain only a type of soliton-like solution. In this paper, we have further found some new multi-soliton solutions and exact travelling solutions of the dispersive long-wave equations from the linear partial equation.

关键词： soliton solution dispersive long-wave equation extended homogeneous balance method

A New Auto-Backlund Transformation and Two-Soliton Solution for (3+l)-Dimensional Jimbo-Miwa Equation

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Communications in Theoretical Physics 2011年第2期55卷 213-216页

作者：刘春平周玲 School of Mathematical Science Yangzhou University

Abstract By improving the extended homogeneous balance method, a general method is suggested to derive a new auto-Bgcklund transformation （BT） for （3-k l）-Dimensional Jimbo-Miwa （JM） equation. The auto-BT obtained by using our method only involves one quadratic homogeneity equation written as a bilinear equation. Based on the auto-BT, two-soliton solution of the （3＋1）-Dimensional JM equation is obtained.

关键词： extended homogeneous balance method (3+1)-Dimensional Jimbo-Miwa equation auto-Backlund transformation exact solution

Backlund transformation and variable separation solutions for the generalized Nozhnik—Novikov—Veselov equation

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Chinese Physics B 2002年第7期11卷 651-655页

作者：张解放 InstituteofNonlinearPhysics ZhejiangNormalUniversityJinhua321004China

Using the extended homogeneous balance method, the Backlund transformation for a (2+1)-dimensional integrablemodel, the generalized Nizhnik-Novikov-Veselov (GNNV) equation, is first obtained. Also, making use of the Ba cklundtransformation, the GNNV equation is changed into three equations: linear, bilinear and trilinear form *** from these three equations, a rather general variable separation solution of the model is constructed. Theabundant localized coherent structures of the model can be induced by the entrance of two variable-separated arbitraryfunctions.

关键词： extended homogeneous balance method (2+1) dimensions GNNV equation localized coherent structures