On the nonlinear self-adjointness and local conservation laws for a class of evolution equations unifying many models

In this paper we consider a class of evolution equations up to fifth-order containing many arbitrary smooth functions from the point of view of nonlinear self-adjointness. The studied class includes many important equations modeling different phenomena. In particular, some of the considered equations were studied previously by other researchers from the point of view of quasi self-adjointness or strictly self-adjointness. Therefore we find new local conservation laws for these equations invoking the obtained results on nonlinearly self-adjointness and the conservation theorem proposed by Nail Ibragimov.