Mathematics

On nonstationary inhomogeneities of the nonlinear 3D Klein — Gordon equation

R. K. Salimov^a, E. G. Ekomasov^ab, A. M. Gumerov<sup>a

a</sup> Bashkir State University, Ufa, Russia
^b South Ural State University, Chelyabinsk, Russia

Abstract: A system of a point material particle and a field described by the nonlinear 3D Klein – Gordon equation is considered. The particle creates nonuniformity of the field and interacts with it. It is showed that when taking into account relativistic effects, if the particle small in comparison with the parameters of nonuniformity of the rest mass, a stable minimum of energy at zero velocity is impossible. Such a behavior is of interest from the point of view of soliton models construction of particles with an intrinsic non-zero moment or soliton models of particles with the oscillating mass.

Keywords: soliton, nonlinear wave equation, relativistic effect.

UDC: 517.958

Received: 19.10.2019
Revised: 05.11.2019

DOI: 10.24411/2500-0101-2019-14405

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