Geodesic
Perturbed soliton solutions of the sine-Gordon equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 12, pp. 2182-2188

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Soliton solutions of the sine-Gordon classical equation are numerically studied. It is shown that considerable perturbations in these solutions lead to the formation of new solution forms that exhibit soliton properties in interactions. The study is performed for kinks and breathers obtained by solving problems with suitable initial data. The underlying numerical technique combines the fourth-order Runge–Kutta method with the quasi-spectral Fourier method. 
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     author = {S. P. Popov},
     title = {Perturbed soliton solutions of the {sine-Gordon} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2182--2188},
     publisher = {mathdoc},
     volume = {49},
     number = {12},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_12_a7/}
}
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S. P. Popov. Perturbed soliton solutions of the sine-Gordon equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 12, pp. 2182-2188. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_12_a7/