Geodesic
Pseudo-spectral Fourier method as applied to finding localized spherical soliton solutions of $(3 + 1)$-dimensional Klein–Gordon equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1628-1634

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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. 
@article{ZVMMF_2016_56_9_a8,
     author = {E. G. Ekomasov and R. K. Salimov},
     title = {Pseudo-spectral {Fourier} method as applied to finding localized spherical soliton solutions of $(3 + 1)$-dimensional {Klein{\textendash}Gordon} equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1628--1634},
     publisher = {mathdoc},
     volume = {56},
     number = {9},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a8/}
}
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E. G. Ekomasov; R. K. Salimov. Pseudo-spectral Fourier method as applied to finding localized spherical soliton solutions of $(3 + 1)$-dimensional Klein–Gordon equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 9, pp. 1628-1634. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_9_a8/