Nonlinear self-adjointness and conservation laws for a generalized Fisher equation

In this work we study a generalization of the well known Fisher equation. We determine the subclasses of these equations which are nonlinear self-adjoint. By using a general theorem on conservation laws proved by Nail Ibragimov and the symmetry generators we find conservation laws for these partial differential equations without classical Lagrangians.

► The generalized Fisher equations are neither quasi self adjoint nor weak self-adjoint.
► The subclasses of nonlinear self-adjoint equations are obtained.
► The conservation laws associated to their Lie symmetries are established.