|Table of Contents|

Solutions of KdV-Burgers and KdV-Burgers-Kuramoto equations by (g’/g2)2 expansion method(PDF)

《纺织高校基础科学学报》[ISSN:1006-6977/CN:61-1281/TN]

Issue:
2016年03期
Page:
327-332
Research Field:
Publishing date:

Info

Title:
Solutions of KdV-Burgers and KdV-Burgers-Kuramoto equations by (g’/g2)2 expansion method
Author(s):
 HE ShuqiCHEN Li
 College of Mathematics, Northwest University, Xi’an 710127, China
Keywords:
(g’/g2)2 expansion method KdV-Burgers equation KdV-Burgers-Kuramoto equation solitary wave solution
PACS:
O 175.29
DOI:
10.13338/j.issn.1006-8341.2016.03.009
Abstract:
Exact solutions of KdV-Burgers equation and KdV-Burgers-Kuramoto equation are obtained by (g’/g2)2 expansion method.Three different types of solutions can be deduced:Hyperbolic function solutions,trigonometric functionsolutions,and rational functional solutions.Solitary wave solution can be calculated when special values of the hyperbolic function solution are properly chosen.From the solving of both equations,it can be concluded that the (g’/g2)2 expansion method is a good choice of solving nonlinear equations which is more convenient,and easy-calculating than (g’/g) expansion method and other methods mentioned before.

References:

[1] WANG M L.Solitary wave solutions for variant Boussinesq equations[J].Physics Letters A,1995,199(3/4):169-172. [2] 刘式适,付遵涛,刘式达,等.变系数非线性方程的Jacobi椭圆函数展开解[J].物理学报,2002,51(9):1923-1926. LIU S S,FU Z T,LIU S D,et al.Jacobi elliptic function expansion solution to the variable coefficient nonlinear equations[J].Acta Physica Sinica,2002,51(9):1923-1926. [3] 张金华,丁玉敏.F展开法结合指数函数法求解Zhiber-Shabat方程的精确解[J].纯粹数学与应用数学,2011,27(2):163-169. ZHANG J H,DING Y M.Combined F-expansion method with Exp-function method for obtaining exact solutions of Zhiber-Shabat equation[J].Pure and Applied Mathematics,2011,27(2):163-169. [4] 朱永平.利用推广的F展开法求解(2+1)维ZK方程[J].纺织高校基础科学学报,2013,26(2):211-213. ZHU Y P.Using expanded F-expansion method for solving(2+1)-dimensional ZK equation[J].Basic Sciences Journal of Textile Universities,2013,26(2):211-213. [5] 陈晓艳,吉飞宇,鱼翔.推广的(G’/G)展开法与Zhiber-Shabat方程的精确解[J].纯粹数学与应用数学,2012,28(4):546-552. CHEN X Y,JI F Y,YU X.Extended (G’/G)-expansion method and exact solutions for Zhiber-Shabat equation[J].Pure and Applied Mathematics,2012,28(4):546-552. [6] LI W A,CHEN H,ZHANG G C.The (w/g)-expansion method and its application to Vakhnenko equation[J].Chinese Physics B,2009,18(2):400-404. [7] WANG M L,LI X Z,ZHANG J L.The (g’/g)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics[J].Physics Letter A,2008,372:417-423. [8] 王振立,李康.(w/g)展开法求解(2+1)维ZK方程的显式解[J].聊城大学学报:自然科学版,2014,27(2):13-16. WANG Z L,LI K.The (w/g)-expansion method and explicit solutions of a(2+1)-dimensional ZK equation[J].Journal of Liaocheng University:Natural Science Edition,2014,27(2):13-16. [9] CHEN J P,CHEN H.The (g’/g2)2-expansion method and its application to coupled nonlinear Klein-Gordon equation[J].Journal of South China Normal University:Natural Science Edition,2012,44(2):63-66. [10] 王思源,陈浩.求解KdV方程和mKdV方程的新方法:(g’/g2)2展开法[J].华南师范大学学报:自然科学版,2014,46(1):42-45. WANG S Y,CHEN H.A new method to solve KdV and mKdV equations by (g’/g2)2 expansion method[J].Journal of South China Normal University:Natural Science Edition,2014,46(1):42-45. [11] 谢元喜,朱曙华.KdV-Burgers方程和KdV-Burgers-Kuramoto方程的精确解[J].安徽大学学报:自然科学版,2007,31(6):44-47. XIE Y X,ZHU S H.Exact solutions to the KdV-Burgers equation and KdV-Burgers-Kuramoto equation[J].Journal of Anhui University:Natural Science Edition,2007,31(6):44-47. [12] 冯庆江,肖绍菊.应用改进的(G’/G2)2展开法求Zakharov方程的精确解[J].量子电子学报,2015,32(1):40-45. FENG Q J,XIAO S J.Derivation of exact solutions for Zakharov equation with extended-(G’/G2)2 expansion method[J].Chinese Journal of Quantum Electronics,2015,32(1):40-45. [13] FENG Q J,LEI X H.Derivation of exact solutions for nonlinear evolution equation with (G’/G2)2-expansion method[J].Mathematica Applicata,2013,26(3):538-543. [14] ZHA Q L,SIRENDAOREJI.Applying the F-expansion method to solve the generalized Nizhnik-Novikov-Veselov equation[J].Acta Scientiarum Naturalium Universitatis Neimongol,2005,36(6):612-617. [15] 冯庆江.应用(G’/G)展开法求Davey-Stewartson I方程的精确解[J].浙江师范大学:自然科学版,2012,35(4):375-380. FENG Q J.Seeking for exact solutions for Davey-Stewartson I equation with (G’/G)-expansion method[J].Journal of Zhejiang Normal University:Natural Science Edition,2012,35(4):375-380. [16] 李德生,张鸿庆.改进的tanh函数方法与广义变系数KdV和MKdV方程新的精确解[J].物理学报,2003,52(7):1569-1573. LI D S,ZHANG H Q.Improved tanh-function method and the new exact solutions for the general variable coefficient KdV equation and MKdV equation[J].Acta Physica Sinica,2003,52(7):1569-1573. [17] 李帮庆,马玉兰.(G’/G)展开法和(2+1)维非对称Nizhnik-Novikov-Veselov系统的新精确解[J].物理学报,2009,58(7):4373-4378. LI B Q,MA Y L.(G’/G)-expansion method and new exact solutions for(2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov system[J].Acta Physica Sinica,2009,58(7):4373-4378.

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Last Update: 2016-10-08