We propose a natural family of higher-order partial differential equations generalizing the second-order Klein-Gordon equation. characterize associated model by means generalized action for scalar field, containing higher-derivative terms. The limit obtained considering arbitrarily powers d'Alembertian operator leading to formal infinite-order equation is discussed. general constructed using ex...

All external electromagnetic fields in which the Klein-Gordon-Fock equation admits first-order symmetry operators are found, provided that space-time V4 a group of motion G3 acts simply transitively on non-null subspace transitivity V3. It is shown case Riemannian space Vn, Gr transitively, algebra n-dimensional an admissible field coincides with Gr.