Nonlinear self-adjointness and conservation laws for some third order equations

Abstract

The concepts of self-adjoint and quasi-self-adjoint equations were introduced by N.H. Ibragimov, he also proved a general theorem on conservation laws. In 2011 the first of these authors has introduced the definition of weak self-adjoint equations and N.H. Ibragimov has introduced the concept of nonlinear self-adjointness. In this paper we consider a generalized Korteweg-de Vries and the third order potential Burgers equation. By using the property of self-adjointness and it generalizations we construct some conservation laws associated with symmetries of the differential equation.