Theoretical and Mathematical Physics

, Volume 167, Issue 3, pp 725–739

New exact solutions of two-dimensional integrable equations using the \(\bar \partial \)-dressing method

  • V. G. Dubrovsky
  • A. V. Topovsky
  • M. Yu. Basalaev
Article

Abstract

We review new classes of exact solutions with functional parameters with constant asymptotic values at infinity of the Nizhnik-Veselov-Novikov equation and new classes of exact solutions with functional parameters of two-dimensional generalizations of the Kaup-Kupershmidt and Sawada-Kotera equations, constructed using the Zakharov-Manakov \(\bar \partial \)-dressing method. We present subclasses of multisoliton and periodic solutions of these equations and give examples of linear superpositions of exact solutions of the Nizhnik-Veselov-Novikov equation.

Keywords

Nizhnik-Veselov-Novikov equation two-dimensional Kaup-Kupershmidt equation two-dimensional Sawada-Kotera equation solutions with functional parameters two-dimensional stationary Schrödinger equation soliton transparent potential 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • V. G. Dubrovsky
    • 1
  • A. V. Topovsky
    • 1
  • M. Yu. Basalaev
    • 1
  1. 1.Novosibirsk State Technical UniversityNovosibirskRussia

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