  The general concept of nonlinear self-adjointness of differential equations
is introduced. It includes the linear self-adjointness as a particular case.
Moreover, it embraces the strict self-adjointness and quasi self-adjointness
introduced earlier by the author. It is shown that the equations possessing the
nonlinear self-adjointness can be written equivalently in a strictly
self-adjoint form by using appropriate multipliers. All linear equations
possess the property of nonlinear self-adjointness, and hence can be rewritten
in a nonlinear strictly self-adjoint. For example, the heat equation $u_t -
\Delta u = 0$ becomes strictly self-adjoint after multiplying by $u^{-1}.$
Conservation laws associated with symmetries can be constructed for all
differential equations and systems having the property of nonlinear
self-adjointness.
