An identity is derived which yields a correspondence between symmetries and conservation
laws for self‐adjoint differential equations. This identity does not rely on use of a Lagrangian
as needed to obtain conservation laws by Noether's theorem. Moreover, unlike Noether's
theorem, which can only generate conservation laws from local symmetries, the derived
identity generates conservation laws from nonlocal as well as local symmetries. It is explicitly
shown how Noether's theorem is extended by the identity. Conservation laws arising from …