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In this work, we have applied a new technique which is a union o f multiplier and Ibragimov’s nonlocal conservation method for constructing the local conservation laws of nonlinear e volution equations. One can conclude that the higher order s olutions of adjoint equation can be obtained by the multiplier function s. The Lax equation and generalized Hirota-Satsuma coupled KdV system are chosen to illustrate the effectiveness of the method. Th us, we have obtained a plenty of local (some of them are the hig her order) conservation laws. The combined method presents a wider app lic bility for handling the conservation laws of nonlinear wave equations.

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