Nonlinear self-adjointness and conservation laws of Klein–Gordon–Fock equation with central symmetry

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The concept of nonlinear self-adjointness, introduced by Ibragimov, has significantly extends approaches to constructing conservation laws associated with symmetries since it incorporates the strict self-adjointness, the quasi self-adjointness as well as the usual linear self-adjointness. Using this concept, the nonlinear self-adjointness condition for the Klein–Gordon–Fock equation was established and subsequently used to construct simplified but infinitely many nontrivial and independent conserved vectors. The Noether’s theorem was further applied to the Klein–Gordon–Fock equation to explore more distinct first integrals, result shows that conservation laws constructed through this approach are exactly the same as those obtained under strict self-adjointness of Ibragimov’s method.