Lie symmetry analysis of the two-dimensional generalized Kuramoto-Sivashinsky equation
1 Department of Mathematics, Karaj Branch, Islamic Azad University, Iran
2 School of Mathematics, Iran University of Science and Technology, Iran
Mathematical Sciences 2012, 6:3 doi:10.1186/2251-7456-6-3Published: 28 May 2012
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.
The basic Lie symmetry method is applied in order to determine the general symmetry group of our analyzed nonlinear model.
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.
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.