Nonlinear self-adjointness and conservation laws

I introduce the general concept of nonlinear self-adjointness. It embraces author's previous notions of strict self-adjointness and quasi self-adjointness. But the set of nonlinearly self-adjoint equations is essentially wider and includes, in particular, all linear equations. The construction of conservation laws demonstrates a practical significance of the nonlinear self-adjointness. Namely, conservation laws can be associated with symmetries for all nonlinearly self-adjoint systems of differential equations. The system can contain any number of equations. This approach provides a new method for constructing conservation laws and extends Noether's theorem from variational problems to arbitrary systems of differential equations. The new theory is illustrated by various applications.