Geodesic
Numerical analysis of soliton solutions of the modified Korteweg–de Vries–sine-Gordon equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 435-445

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Multisoliton solutions of the modified Korteweg–de Vries–sine-Gordon equation (mKdV-SG) are found numerically by applying the quasi-spectral Fourier method and the fourth-order Runge–Kutta method. The accuracy and features of the approach are determined as applied to problems with initial data in the form of various combinations of perturbed soliton distributions. Three-soliton solutions are obtained, and the generation of kinks, breathers, wobblers, perturbed kinks, and nonlinear oscillatory waves is studied. 
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     author = {S. P. Popov},
     title = {Numerical analysis of soliton solutions of the modified {Korteweg{\textendash}de} {Vries{\textendash}sine-Gordon} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {435--445},
     publisher = {mathdoc},
     volume = {55},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_3_a7/}
}
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S. P. Popov. Numerical analysis of soliton solutions of the modified Korteweg–de Vries–sine-Gordon equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 435-445. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_3_a7/