Abstract
•Conservation laws of the KGF equation with central symmetry are explored using Ibragimov’s method and Noether’s theorem.•Nonlinear self-adjointness condition for the KGF equation was established and used to construct many conservation laws.•Conservation laws obtained by the Noether’s theorem are special cases of those obtained by Ibragimov’s method.•Obtained conserved vectors are nontrivial, independent and infinite.
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.