Conservation laws for a class of quasi self-adjoint third order equations

摘要

In this work we consider a class of third-order nonlinear partial differential equation containing two un-specified coefficient functions of the dependent variable which include various integrable and nonintegrable equations. We determine the subclasses of these equations which are self-adjoint and quasi self-adjoint. By using a general theorem on conservation laws proved by Nail Ibragimov we find conservation laws for some of these partial differential equations without classical Lagrangians.