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Zh. Vychisl. Mat. Mat. Fiz., 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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:2, 314–322

Bibliographic databases:

UDC: 519.634
Received: 11.04.2008

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Nazarov S.A., “Localized elastic fields in periodic waveguides with defects”, J. Appl. Mech. Tech. Phys., 52:2 (2011), 311–320  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
    2. M. I. Fakhretdinov, F. K. Zakiryanov, E. G. Ekomasov, “Diskretnye brizery i multibrizery v modeli DNK Peirara–Bishopa”, Nelineinaya dinam., 11:1 (2015), 77–87  mathnet  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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