Infinite series symmetry reduction solutions to the modified KdV-Burgers equation  

作　　者：姚若侠 焦小玉 楼森岳 

机构地区：[1]Department of Physics,Shanghai Jiao Tong University [2]School of Computer Science,Shaanxi Normal University [3]Department of Physics,Ningbo University

出　　处：《Chinese Physics B》2009年第5期1821-1827,共7页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundations of China(Grant Nos 10735030,10475055,and 90503006);the National Basic Research Program of China(Grant No 2007CB814800);the Science Foundation for Post Doctorate Research from the Ministry of Science and Technology of China(Grant No 20070410727);the Natural Science Basic Research Plan in Shaanxi Province,China(Grant No SJ08A09)

摘　　要：From the point of view of approximate symmetry, the modified Korteweg-de Vries-Burgers （mKdV-Burgers） equation with weak dissipation is investigated. The symmetry of a system of the corresponding partial differential equations which approximate the perturbed mKdV-Burgers equation is constructed and the corresponding general approximate symmetry reduction is derived; thereby infinite series solutions and general formulae can be obtained. The obtained result shows that the zero-order similarity solution to the mKdV-Burgers equation satisfies the Painleve II equation. Also, at the level of travelling wave reduction, the general solution formulae are given for any travelling wave solution of an unperturbed mKdV equation. As an illustrative example, when the zero-order tanh profile solution is chosen as an initial approximate solution, physically approximate similarity solutions are obtained recursively under the appropriate choice of parameters occurring during computation.From the point of view of approximate symmetry, the modified Korteweg-de Vries-Burgers （mKdV-Burgers） equation with weak dissipation is investigated. The symmetry of a system of the corresponding partial differential equations which approximate the perturbed mKdV-Burgers equation is constructed and the corresponding general approximate symmetry reduction is derived; thereby infinite series solutions and general formulae can be obtained. The obtained result shows that the zero-order similarity solution to the mKdV-Burgers equation satisfies the Painleve II equation. Also, at the level of travelling wave reduction, the general solution formulae are given for any travelling wave solution of an unperturbed mKdV equation. As an illustrative example, when the zero-order tanh profile solution is chosen as an initial approximate solution, physically approximate similarity solutions are obtained recursively under the appropriate choice of parameters occurring during computation.

关 键 词：modified Korteweg-de Vries-Burgers （mKdV-Burgers） equation approximate symme-try reduction series reduction solution 

分 类 号：O411.1[理学—理论物理] O175[理学—物理]