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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 2, Pages 323–331 (Mi zvmmf43)  
This article is cited in 2 scientific papers (total in 2 papers)

On the shapes of two-dimensional soliton perturbations in simple lattices

S. P. Popov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
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Abstract: 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.
Key words: two-dimensional Toda lattice, discrete Korteweg–de Vries equation, integrable dynamical system, soliton, numerical solution.
Received: 11.04.2008
English version:
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 2, Pages 314–322
DOI: https://doi.org/10.1134/S0965542509020110
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: S. P. Popov, “On the shapes of two-dimensional soliton perturbations in simple lattices”, Zh. Vychisl. Mat. Mat. Fiz., 49:2 (2009), 323–331; Comput. Math. Math. Phys., 49:2 (2009), 314–322
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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