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

Nonlinear Klein-Gordon equations with fractional power and logarithmic potentials and with a variation in the phi(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.