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.

A succinct presentation of the algebraic structure of the quantized Klein-Gordon field can be given in terms of a Lorentz invariant inner product. A presentation of a classical Klein-Gordon random field at non-zero temperature can be given in the same noncommutative algebraic style, allowing a detailed comparison of the quantized Klein-Gordon field with a classical Klein-Gordon random field.

We study local well-posedness and orbital stability/instability of standing waves for a first order system associated with nonlinear Klein–Gordon equation on star graph. The proof the uses classical fixed point argument Hille–Yosida theorem. Stability relies linearization approach recent results NLS ?-interaction

We obtain exact solutions of the (1+1) dimensional Klein Gordon equation with linear vector and scalar potentials in the presence of a minimal length. Algebraic approach to the problem has also been studied.