Geodesic
On the shapes of two-dimensional soliton perturbations in simple lattices
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 323-331

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The Toda lattice and the discrete Korteweg–de Vries equation generalized to two dimensions are studied numerically. The interactions are assumed to be identical in both directions. It is shown that the equations have solutions in the form of plane linear and localized solitons. In contrast to equations integrable by the inverse scattering method, the parameters of solitons change in the course of their interaction and additional wave structures are formed. The basic types of solutions characterizing these processes are presented. 
@article{ZVMMF_2009_49_2_a10,
     author = {S. P. Popov},
     title = {On the shapes of two-dimensional soliton perturbations in simple lattices},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {323--331},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a10/}
}
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S. P. Popov. On the shapes of two-dimensional soliton perturbations in simple lattices. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 323-331. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a10/