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Rapidly oscillating solutions of a generalized Korteweg–de Vries equation

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Abstract

For a generalized Korteweg–de Vries equation, the existence of families of rapidly oscillating periodic solutions is proved and their asymptotic representation is found. The asymptotics of tori of different dimensions are examined. Formulas for solutions depending on all parameters of the problem are derived.

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Authors and Affiliations

  1. Yaroslavl State University, Yaroslavl, 150000, Russia

    S. A. Kashchenko

  2. National Research Nuclear University “MEPhI,”, Moscow, 115409, Russia

    S. A. Kashchenko

Authors
  1. S. A. Kashchenko
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Correspondence to S. A. Kashchenko.

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Original Russian Text © S.A. Kashchenko, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 11, pp. 1812–1823.

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Kashchenko, S.A. Rapidly oscillating solutions of a generalized Korteweg–de Vries equation. Comput. Math. and Math. Phys. 57, 1778–1788 (2017). https://doi.org/10.1134/S0965542517110082

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  • DOI: https://doi.org/10.1134/S0965542517110082

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