Geodesic
Limiting solitons and kinks in two-dimensional discrete systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 792-799

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Two-dimensional discrete equations of the first order in time are considered. Each element of the lattice is assumed to interact only with the nearest neighbors and the interaction force tends to a constant for large deviations from the equilibrium. Localized solitary waves (solitons) and kinks whose amplitudes and velocities do not exceed the limiting values are numerically found. The cases of pair interactions are examined. 
@article{ZVMMF_2013_53_5_a9,
     author = {S. P. Popov},
     title = {Limiting solitons and kinks in two-dimensional discrete systems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {792--799},
     publisher = {mathdoc},
     volume = {53},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_5_a9/}
}
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S. P. Popov. Limiting solitons and kinks in two-dimensional discrete systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 792-799. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_5_a9/