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A connection between the(G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation 被引量:3
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作者 赵银龙 柳银萍 李志斌 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第3期41-46,共6页
Recently the (G′/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the (G′/G)-expansion method is a special form of the truncated Pain... Recently the (G′/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the (G′/G)-expansion method is a special form of the truncated Painlev'e expansion method by introducing an intermediate expansion method. Then the generalized (G′/G)-(G/G′) expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev'e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the ( G′/ G)-expansion method. 展开更多
关键词 (G′/G)-expansion method truncated Painlev'e expansion method mKdV equation trav-eling wave solutions
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NEW TRUNCATED EXPANSION METHOD AND SOLITON-LIKE SOLUTION OF VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNCTIONS
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作者 张解放 刘宇陆 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第11期1259-1263,共5页
The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coef... The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated. 展开更多
关键词 variable coefficient nonlinear evolution equation soliton-like solution truncated expansion method
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New Exact Solutions for Benjamin-Bona-Mahony-Burgers Equation 被引量:2
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作者 Chunhuan Xiang Honglei Wang 《Open Journal of Applied Sciences》 2020年第8期543-550,共8页
Obtaining the new solutions for the nonlinear evolution equation is a hot topic. Benjamin<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-... Obtaining the new solutions for the nonlinear evolution equation is a hot topic. Benjamin<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Bona</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Mahony</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Burgers equation is this kind of equation,</span></span></span><span><span><b><span style="font-family:""> </span></b></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">t</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">he solutions are very interest. Several new exact solutions for the nonlinear equation are obtained by using truncated expansion method in this paper. The numerical simulations with different parameters for the new exact solutions of Benjamin</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Bona</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Mahony</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">Burgers equation are given.</span></span></span> 展开更多
关键词 Truncated expansion method Benjamin-Bona-Mahony-Burgers Equation EVOLUTION Nonlinear Equation
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Some Remarks on Exp-Function Method and Its Applications-A Supplement 被引量:1
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作者 smail Aslan 《Communications in Theoretical Physics》 SCIE CAS CSCD 2013年第11期521-525,共5页
Recently,the authors of[Commun.Theor.Phys.56(2011)397]made a number of useful observations on Exp-function method.In this study,we focus on another vital issue,namely,the misleading results of double Exp-function method.
关键词 Exp-function method Cahn-Allen equation truncated (Painleve) expansion method
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Various Kinds Waves and Solitons Interaction Solutions of Boussinesq Equation Describing Ultrashort Pulse in Quadratic Nonlinear Medium 被引量:2
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作者 Bang-Xing Guo Zhan-Jie Gao Ji Lin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2016年第12期589-594,共6页
The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explici... The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves. 展开更多
关键词 soliton interaction Boussinesq equation consistent tanh expansion method Painlevé truncated expansion method
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