Geodesic
Soliton solutions to generalized discrete Korteweg–de Vries equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1698-1709

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New discrete equations of the simplest three-point form are considered that generalize the discrete Korteweg–de Vries equation. The properties of solitons, kinks, and oscillatory waves are numerically examined for three types of interactions between neighboring chain elements. An analogy with solutions to limiting continual equations is drawn. 
@article{ZVMMF_2008_48_9_a13,
     author = {S. P. Popov},
     title = {Soliton solutions to generalized discrete {Korteweg{\textendash}de} {Vries} equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1698--1709},
     publisher = {mathdoc},
     volume = {48},
     number = {9},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a13/}
}
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S. P. Popov. Soliton solutions to generalized discrete Korteweg–de Vries equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1698-1709. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a13/