Abstract
Nonlinear self-adjointness method for constructing conservation laws of partial differential equations (PDEs) is further studied. We show that any adjoint symmetry of PDEs is a differential substitution of nonlinear self-adjointness and vice versa. Consequently, each symmetry of PDEs corresponds to a conservation law via a formula if the system of PDEs is nonlinearly self-adjoint with differential substitution. As a byproduct, we find that the set of differential substitutions includes the set of conservation law multipliers as a subset. The results are illustrated by three typical examples.
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