This article is cited in 1 paper

Pseudo-spectral Fourier method as applied to finding localized spherical soliton solutions of $(3 + 1)$-dimensional Klein–Gordon equations

E. G. Ekomasov, R. K. Salimov

Bashkir State University, Ufa, Bashkortostan, Russia

Abstract: Nonlinear Klein–Gordon equations with fractional power and logarithmic potentials and with a variation in the $\varphi^4$ potential are found for which the existence of long-lived stable spherically symmetric solutions in the form of pulsons is numerically established. Their mean oscillation amplitude and the frequency of the fast oscillation mode do not vary in the course of the numerical simulation. It is shown that the stability of these pulsons is explained by the presence of a potential well.

Key words: Klein–Gordon equation, pulson, breather, pseudospectral Fourier method.

UDC: 519.634

Received: 01.01.2015

DOI: 10.7868/S0044466916090052

 English version: Computational Mathematics and Mathematical Physics, 2016, 56:9, 1604–1610

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