Interacting Localized Solutions of the Nonlinear Klein—Gordon Equation with a Variable Mass

A system consisting of material particles and a field is studied. The latter is described by the nonlinear Klein—Gordon equation. A modified Klein—Gordon equation, which allows the solutions of the Klein—Gordon equation with both zero and nonzero masses, is considered. Particles give rise to field inhomogeneities and interact with the field. It is shown that stable oscillating localized solutions are possible in this model. The oscillating localized solutions in this system generate traveling waves, leading to the interaction of these solutions at large distances.