Symmetries and conservation laws of evolution equations via multiplier and nonlocal conservation methods

Abstract

Abstract:In this work, we have applied a new technique which is a union of multiplier and Ibragimov's nonlocal conservation method for constructing the local conservation laws of nonlinear evolution equations. One can conclude that the higher order solutions of adjoint equation can be obtained by the multiplier functions. The Lax equation and generalized Hirota-Satsuma coupled KdV system are chosen to illustrate the effectiveness of the method. Thus, we have obtained a plenty of local (some of them are the higher order) conservation laws. The combined method presents a wider applicability for handling the conservation laws of nonlinear wave equations.