Lie symmetry analysis of the two-dimensional generalized Kuramoto-Sivashinsky equation

被引：4
|
作者：
Nadjafikhah M. [1 ]
Ahangari F. [2 ]
机构：
[1] Department of Mathematics, Karaj Branch, Islamic Azad University
[2] School of Mathematics, Iran University of Science and Technology
来源：
Mathematical Sciences | 2012年 / 6卷 / 1期
关键词：
Invariant solutions; Lie symmetry method; Optimal system; Similarity reduced equations; Two dimensional generalized Kuramoto-Sivanshsky (2D gKS) equation;
D O I：
10.1186/2251-7456-6-3
中图分类号：
学科分类号：
摘要：
Purpose: In this paper, a detailed analysis of an important nonlinear model system, the two dimensional generalized Kuramoto-Sivashinsky (2D gKS) equation, is presented by group analysis. Methods: The basic Lie symmetry method is applied in order to determine the general symmetry group of our analyzed nonlinear model. Results: The symmetry group of the equation and some results related to the algebraic structure of the Lie algebra of symmetries are obtained. Also, a complete classification of the subalgebras of the symmetry algebra is resulted. Conclusions: It is proved that the Lie algebra of symmetries admits no three dimensional subalgebra. Mainly, all the group invariant solutions and the similarity reduced equations associated to the infinitesimal symmetries are obtained. © 2012, Nadjafikhah and Ahangari; licensee Springer.
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