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A Modified Homogeneous Balance Method and Its Applications 被引量:1
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作者 刘春平 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第8期223-227,共5页
A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbala... A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbalance method.Generalized Boussinesq equation,KP equation,and mKdV equation are chosen as examples to illustrateour method.This approach is also applicable to a large variety of nonlinear evolution equations. 展开更多
关键词 homogeneous balance method bilinear equation generalized Boussinesq equation KP equation mKdV equation
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Exact Solutions for the Generalized KdV Equation: Modified Homogeneous Balance Method
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作者 WANG Xiu-mei ZHU Yue-feng 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第2期260-269,共10页
In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several ki... In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several kinds of exact(new) solutions of the generalized KdV equation are obtained. 展开更多
关键词 generalized KdV equation modified homogeneous balance method exact solutions
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A new auxiliary equation method for finding travelling wave solutions to KdV equation 被引量:3
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作者 庞晶 边春泉 朝鲁 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第7期929-936,共8页
In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the (1+1)-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which... In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the (1+1)-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which cover the existing solutions. Compared to other methods, the presented method is more direct, more concise, more effective, and easier for calculations. In addition, it can be used to solve other nonlinear evolution equations in mathematical physics. 展开更多
关键词 auxiliary equation method travelling wave solution KdV equation homogeneous balance method
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Homogenous Balance Method and Exact Analytical Solutions for Whitham-Broer-Kaup Equations in Shallow Water 被引量:1
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作者 XIAZhi 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第3期240-246,共7页
Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and... Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations. 展开更多
关键词 improved homogenous balance method Backlund transformation solitary wave solution multiple solution exact analytical solution rational solution
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The (G'/G, 1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations 被引量:13
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作者 LI Ling-xiao LI Er-qiang WANG Ming-liang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第4期454-462,共9页
The (G'/G, 1/G)-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the (G'/G)-expansion method proposed recently, is present... The (G'/G, 1/G)-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the (G'/G)-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves. 展开更多
关键词 The (G /G 1/G)-expansion method travelling wave solutions homogeneous balance solitary wave solutions Zakharov equations.
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A Simplified Hirota Method and Its Application
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作者 徐桂琼 张善卿 李志斌 《Journal of Shanghai University(English Edition)》 CAS 2003年第2期143-147,共5页
By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential... By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential equation with this nonlinear transformation. By solving the homogeneity equation via the simplified Hirota method and applying the nonlinear transformation, one soliton, two soliton and three soliton solutions as well as some other types of explicit solutions to the breaking soliton equation were obtained with the assistance of Maple. 展开更多
关键词 the homogeneous balance principle simplified Hirota method soliton solution the breaking soliton equation.
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Auto-Backlund Transformation and Extended Tanh-Function Methods to Solve the Time-Dependent Coefficients Calogero-Degasperis Equation
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作者 Rehab M. El-Shiekh 《American Journal of Computational Mathematics》 2015年第2期215-223,共9页
In this paper, the Auto-B?cklund transformation connected with the homogeneous balance method (HB) and the extended tanh-function method are used to construct new exact solutions for the time-dependent coefficients Ca... In this paper, the Auto-B?cklund transformation connected with the homogeneous balance method (HB) and the extended tanh-function method are used to construct new exact solutions for the time-dependent coefficients Calogero-Degasperis (VCCD) equation. New soliton and periodic solutions of many types are obtained. Furthermore, the soliton propagation is discussed under the effect of the variable coefficients. 展开更多
关键词 Auto-Backlund Transformation homogeneous Balance method The Extended Tanh-Function method The Time-Dependent Coefficients Calogero-Degasperis Equation Exact Solutions
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Exotic Localized Coherent Structures of the (2+1)—Dimensional Dispersive Long—Wave Equation 被引量:11
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作者 ZHANGJie-Fang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2002年第3期277-282,共6页
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 ba... 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. 展开更多
关键词 extended homogeneous balance method coherent soliton structures dispersive long-wave equation the (2+1)-dimensions
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Some Special Types of Solitary Wave Solutions for (3+1)-Dimensional Jimbo-MiwaEquation 被引量:3
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作者 BAICheng-Lin ZHAOHong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第6期875-877,共3页
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
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AUTO-DARBOUX TRANSFORMATION AND EXACT SOLUTIONS OF THE BRUSSELATOR REACTION DIFFUSION MODEL 被引量:2
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作者 YAN Zhenya(闫振亚) +1 位作者 ZHANG Hongqing(张鸿庆) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第5期541-546,共6页
Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain ... Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method, more exact solutions are found which contain soliton solutions. 展开更多
关键词 brusselator reaction model Darboux transformation homogeneous balance method sine-cosine method exact solution
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Oscillating Solitons for (2+1)-Dimensional Nonlinear Models 被引量:2
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作者 Naranmandula Tubuxin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第2期282-286,共5页
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... 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. 展开更多
关键词 oscillating soliton (2+1)-dimensional system extended homogeneous balance method
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A New Auto-Backlund Transformation and Two-Soliton Solution for (3+l)-Dimensional Jimbo-Miwa Equation 被引量:1
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作者 刘春平 周玲 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第2期213-216,共4页
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 obtain... 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. 展开更多
关键词 extended homogeneous balance method (3+1)-Dimensional Jimbo-Miwa equation auto-Backlund transformation exact solution
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On an Auto-Baecklund Transformation for (2+1)-Dimensional VariableCoefficient Generalized KP Equations and Exact Solutions 被引量:1
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作者 BAICheng-Jie BAICheng-Lin +1 位作者 HANJi-Guang ZHAOHong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第4期677-680,共4页
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 ... 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 homogeneity equations to be solved, we obtainsome exact solutions containing single solitary waves. 展开更多
关键词 extended homogeneous balance method (2+1)-dimensional variable coefficientgeneralized KP equation auto-Baecklund transformation exact solutions
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Bcklund Transformation and Localized Coherent Structure for the (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov Equation 被引量:1
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作者 张解放 刘宇陆 《Journal of Shanghai University(English Edition)》 CAS 2002年第3期191-195,共5页
This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structure of the (2+1) dimensional asymmetric Nizhnik Novikov Veselov equation. A B a¨... This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structure of the (2+1) dimensional asymmetric Nizhnik Novikov Veselov equation. A B a¨ cklund transformation was first obtained, and then the richness of the localized coherent structures was found, which was caused by the entrance of two variable separated arbitrary functions, in the model. For some special choices of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, and ring solitons. 展开更多
关键词 homogeneous balance method coherent soliton structures asymmetric Nizhnik Novikov veselov equation (ANNV equation) B cklund transformation.
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Vortex Spatial Solitons to a Nonlinear Schrodinger Equation with Varying Coefficients 被引量:1
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作者 徐四六 梁检初 李忠明 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第12期1105-1110,共6页
Based on homogeneous balance method, sofiton solutions to a generalized nonlinear Sehr6dinger equation (NLSE) with varying coefficients have been gotten. Our results indicate that a new family of vortex or petal-lik... Based on homogeneous balance method, sofiton solutions to a generalized nonlinear Sehr6dinger equation (NLSE) with varying coefficients have been gotten. Our results indicate that a new family of vortex or petal-like spatial solitons can be formed in the Kerr nonlinear media in the cylindrical symmetric geometry. It is shown by numerical simulation that these soliton profiles are stable. 展开更多
关键词 optic soliton homogeneous balance method
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New Explicit Exact Solutions to (2+1)-Dimensional Generalized Broer-Kaup System
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作者 HUANGDing-Jiang ZHANGHong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第3期397-400,共4页
A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear tran... A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear transformation, we reduce the (2+ 1)-dimensional GBK system to a simple linear evolution equation. Solving this equation,we can obtain some new explicit exact solutions of the original equations by means of the extended hyperbola function method. 展开更多
关键词 generalized Broer-Kaup system nonlinear transformation exact solutions homogeneous balance method hyperbola function method
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STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS
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作者 YAN Zhen-ya(闫振亚) +1 位作者 ZHANG Hong-qing(张鸿庆) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第8期925-934,共10页
The homogeneous balance method was improved and applied to two systems Of nonlinear evolution equations. As a result, several families of exact analytic solutions are derived by some new ansatzs. These solutions conta... The homogeneous balance method was improved and applied to two systems Of nonlinear evolution equations. As a result, several families of exact analytic solutions are derived by some new ansatzs. These solutions contain Wang's and Zhang's results and other new types of analytical solutions, such as rational fraction solutions and periodic solutions. The way can also be applied to solve more nonlinear partial differential equations. 展开更多
关键词 nonlinear evolution equations improved homogeneous balance method exact analytical solution solitary wave solution rational solution
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New Exact Solutions and Special Coherent Structures for Coupled Integrable Dispersionless Equation
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作者 Naranmandula 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第6期1037-1041,共5页
Using improved homogeneous balance method, we obtain new exact solutions for the coupled integrable dispersionless equation. On the basis of these exact solutions, we find some new interesting coherent structures by s... Using improved homogeneous balance method, we obtain new exact solutions for the coupled integrable dispersionless equation. On the basis of these exact solutions, we find some new interesting coherent structures by selecting arbitrary functions appropriately. 展开更多
关键词 exact solution coherent structure coupled integrable dispersionless equation improved homogeneous balance method
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LOCALIZED COHERENT STRUCTURES OF THE (2+1)-DIMENSIONAL HIGHER ORDER BROER-KAUP EQUATIONS
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作者 ZHANG Jie-fang(张解放) +1 位作者 LIU Yu-lu(刘宇陆) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第5期549-556,共8页
By using the extended homogeneous balance method, the localized coherent structures are studied. A nonlinear transformation was first established, and then the linearization form was obtained based on the extended hom... By using the extended homogeneous balance method, the localized coherent structures are studied. A nonlinear transformation was first established, and then the linearization form was obtained based on the extended homogeneous balance method for the higher order (2 + 1)-dimensional Broer-Kaup equations. Starting from this linearization form equation, a variable separation solution with the entrance of some arbitrary functions and some arbitrary parameters was constructed. The quite rich localized coherent structures were revealed. This method, which can be generalized to other (2 + I) -dimensional nonlinear evolution equation, is simple and powerful. 展开更多
关键词 higher order Broer-Kaup equation (2+1)-dimension coherent structure homogeneous balance method
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Nonlinear ion-acoustic solitary waves in an electron-positron-ion plasma with relativistic positron beam
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作者 Ridip Sarma Amar P Misra Nirab C Adhikary 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第10期471-476,共6页
The propagation characteristics of nonlinear ion–acoustic(IA) solitary waves(SWs) are studied in thermal electron–positron–ion plasma considering the effect of relativistic positron beam. Starting from a set of... The propagation characteristics of nonlinear ion–acoustic(IA) solitary waves(SWs) are studied in thermal electron–positron–ion plasma considering the effect of relativistic positron beam. Starting from a set of fluid equations and using the reductive perturbation technique, we derive a Korteweg–de Vries(KdV) equation which governs the evolution of weakly nonlinear IA SWs in relativistic beam driven plasmas. The properties of the IA soliton are studied, and it is shown that the presence of relativistic positron beam significantly modifies the characteristics of IA solitons. 展开更多
关键词 electron-positron-ion plasma relativistic effect ion-acoustic wave homogeneous balance method
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