Geodesic
Transformation of sine-Gordon solitons in models with variable coefficients and damping
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 631-640

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The dynamics of sine-Gordon solitons in the presence of an external force, damping, and a spatially modulated periodic potential is studied. Numerical methods are used to show the possibility of generating localized nonlinear waves of the soliton and breather types. Their evolution is investigated, and the dependences of the amplitude and the oscillation frequency on the parameters of the system are found. 
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     author = {A. M. Gumerov and E. G. Ekomasov and R. R. Murtazin and V. N. Nazarov},
     title = {Transformation of {sine-Gordon} solitons in models with variable coefficients and damping},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
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     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a10/}
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A. M. Gumerov; E. G. Ekomasov; R. R. Murtazin; V. N. Nazarov. Transformation of sine-Gordon solitons in models with variable coefficients and damping. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 631-640. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a10/