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通过采用一种新的方法来求解Camassa-Holm(CH)方程的行波解,得到较为丰富的周期波解、孤立波解,并到得了一些新的具有椭圆函数形式的精确行波解。
Abstract:A new method is used to work out the traveling wave solutions of CH equation.Many periodic and soliton solutions of CH equation are successfully obtained,and new exact traveling wave solutions have been obtained in elliptic function terms.
[1]刘式适,付遵涛,刘式达,等.一类非线性方程的新周期解[J].物理学报,2002,51:10-14.
[2]王明亮.非线性发展方程与孤立子[M].兰州:兰州大学出版社,1990.
[3]谷超豪.孤立子理论与应用[M].杭州:浙江科学技术出版社,1990.
[4]李志斌.非线性物理方程的行波解[M].北京:科技出版社,2007.
[5]王明亮,李志斌,周宇斌.齐次平衡原则及其应用[J].兰州大学学报,1999,35:8-16.
[6]闫振亚.一类非线性演化方程新的显式行波解[J].物理学报,1999,48:1-5.
[7]刘式适,付遵涛,刘式达,等.求某些非线性偏微分方程特解的一个简洁方法[J].应用数学和力学,2001,22:281-286.
[8]刘式达,刘式适,叶其孝.非线性演化方程的显式行波解[J].数学的实践与认识,1998,28:289-301.
[9]楼森岳.推广的Painlevé展开及非标准截断解[J].物理学报,1998,47:1739-1745.
[10]HE J H.Application of homotopy perturbation method tononlinear wave equations[J].Chaos,Solitons&Fractals,2005,26:695-700.
[11]李志斌,张善卿.非线性波方程准确孤立波解的符号计算[J].数学物理学报,1997,17(1):81-89.
[12]YUSUFOGLU E.New solitonary solutions for modified formsof DP and CH equa-tions using Exp-function method[J].Chaos,Solitons&Fractals,2007,10:703-706.
[13]ABBASBANDY S.Solitary wave solutions to the modifiedform of Camassa-Holm equation by means of the homotopyanalysis method[J].Chaos,Solitons&Fractals,2009,39:428-435.
[14]FENG Z S.Standard forms of elliptic integrals and theirapplications to nonlinear evolution equations[J].Chaos,Solitons&Fractals,2005,25:177-184.
[15]DING S.A new method for finding traveling wave solutions ofthe generalized KdV equation with variable coefficient[J].Applied Mathematics and Computation,2008,199:268–274.
基本信息:
DOI:
中图分类号:O175.29
引用信息:
[1]赵小山,李震波.Camassa-Holm方程丰富的行波解[J].天津职业技术师范大学学报,2011,21(01):65-66+70.
基金信息:
国家自然科学基金资助项目(10802061)