广义变系数Kuramoto-Sivashinsky方程的显式解

J4 ›› 2015, Vol. 32 ›› Issue (4): 419-424.

广义变系数Kuramoto-Sivashinsky方程的显式解

李康，刘希强

聊城大学数学科学学院，山东聊城 252059

收稿日期:2014-12-31 修回日期:2015-03-28 出版日期:2015-07-28 发布日期:2015-08-04
通讯作者: 刘希强 (1957-)山东，教授，博士，从事非线性发展方程系统 E-mail:liuxq@sina.com
作者简介:李康(1989-),女，山东德州人，硕士生，主要从事非线性发展方程求解研究,E-mail:873481015@qq.com
基金资助:
国家自然科学基金与中国工程物理研究院基金课题（11076015）

Explicit solutions of the generalized Kuramoto-Sivashinsky equation with variable coefficients

LI Kang, LIU Xi-qiang

School of Mathematicas Science, Liao Cheng University, Liaocheng 252059, China

Received:2014-12-31 Revised:2015-03-28 Published:2015-07-28 Online:2015-08-04

摘要/Abstract

摘要：

应用修正的CK直接约化方法,得到了广义变系数Kuramoto-Sivashinsky方程与其对应的常系数方程解之间的关系,利用李群方法得到了常系数Kuramoto-Sivashinsky方程的一些显式解,从而获得了广义变系数Kuramoto-Sivashinsky方程的新解.

关键词: 广义变系数Kuramoto-Sivashinsky方程;CK方法;对称约化;精确解

Abstract:

By using the improved CK’s method, the relation between the generalized Kuramoto-Sivashinsky equation with variable coefficient and the corresponding coefficient. Some new exact solutions of the corresponding constant coefficient equation are obtained by applying the Lie group method, and then get the explicit solutions of the generalized Kuramoto-Sivashinsky equation with variable coefficients.

Key words: generalized Kuramoto-Sivashinsky equation, modified CK’s direct method, symmetry, exact solutions

李康，刘希强. 广义变系数Kuramoto-Sivashinsky方程的显式解[J]. J4, 2015, 32(4): 419-424.

LI Kang, LIU Xi-qiang. Explicit solutions of the generalized Kuramoto-Sivashinsky equation with variable coefficients[J]. J4, 2015, 32(4): 419-424.

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