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Soliton solutions to generalized discrete Korteweg-de Vries equations

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Abstract

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.

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Authors and Affiliations

  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    S. P. Popov

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  1. S. P. Popov
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Correspondence to S. P. Popov.

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Original Russian Text © S.P. Popov, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 9, pp. 1698–1709.

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Popov, S.P. Soliton solutions to generalized discrete Korteweg-de Vries equations. Comput. Math. and Math. Phys. 48, 1658–1668 (2008). https://doi.org/10.1134/S0965542508090145

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  • DOI: https://doi.org/10.1134/S0965542508090145

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