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Russian Physics Journal

, Volume 58, Issue 7, pp 930–940 | Cite as

Solutions with Functional Parameters of 2+1-Dimensional Integrable Nonlinear Equations. Two Dimensional Integrable Generalization of the Kaup–Kupershmidt Equation

  • V. G. Dubrovsky
  • A. V. Topovsky
  • M. Yu. Basalaev
ELEMENTARY PARTICLE PHYSICS AND FIELD THEORY

With the help of the Zakharov–Manakov \( \overline{\partial} \) -dressing method, new classes of exact solutions with functional parameters of a two-dimensional integrable generalization of the Kaup–Kupershmidt equation have been constructed. It is shown that the constructed solutions contain soliton solutions and a subclass of new periodic solutions. Nonsingular solutions are also present among the constructed periodic solutions.

Keywords

integrable nonlinear equations the \( \overline{\partial} \) -dressing method two-dimensional integrable generalization of the Kaup–Kupershmidt equation solutions with functional parameters periodic solutions 

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Copyright information

© Springer Science+Business Media New York 2015

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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