Geodesic
Scattering of solitons by dislocations in the modified Korteweg de Vries–sine-Gordon equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2055-2066

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Multisoliton solutions of the modified Korteweg de Vries–sine-Gordon equation involving coefficients with local perturbations in the coordinate are considered. Cases describing the bifurcation regimes of reflection and capture of solitons (kinks and breathers) in their interaction with dislocations of various Gaussian forms are numerically studied. 
@article{ZVMMF_2015_55_12_a8,
     author = {S. P. Popov},
     title = {Scattering of solitons by dislocations in the modified {Korteweg} de {Vries{\textendash}sine-Gordon} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2055--2066},
     publisher = {mathdoc},
     volume = {55},
     number = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a8/}
}
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S. P. Popov. Scattering of solitons by dislocations in the modified Korteweg de Vries–sine-Gordon equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2055-2066. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a8/