Symmetry Reduction of Two-Dimensional Damped Kuramoto-Sivashinsky Equation

In this paper,the problem of determining the largest possible set of symmetries for an important nonlineardynamical system: the two-dimensional damped Kuramoto-Sivashinsky ((2D) DKS ) equation is studied.By applyingthe basic Lie symmetry method for the (2D) DKS equation,the classical Lie point symmetry operators are obtained.Also,the optimal system of one-dimensional subalgebras of the equation is constructed.The Lie invariants as well assimilarity reduced equations corresponding to infinitesimal symmetries are obtained.The nonclassical symmetries of the(2D) DKS equation are also investigated.