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Regular and Chaotic Dynamics

, Volume 16, Issue 6, pp 562–576 | Cite as

Point vortices and polynomials of the Sawada-Kotera and Kaup-Kupershmidt equations

  • Maria V. Demina
  • Nikolai A. Kudryashov
Article

Abstract

Rational solutions and special polynomials associated with the generalized K 2 hierarchy are studied. This hierarchy is related to the Sawada-Kotera and Kaup-Kupershmidt equations and some other integrable partial differential equations including the Fordy-Gibbons equation. Differential-difference relations and differential equations satisfied by the polynomials are derived. The relationship between these special polynomials and stationary configurations of point vortices with circulations Γ and −2Γ is established. Properties of the polynomials are studied. Differential-difference relations enabling one to construct these polynomials explicitly are derived. Algebraic relations satisfied by the roots of the polynomials are found.

Keywords

point vortices special polynomials generalized K2 hierarchy Sawada-Kotera equation Kaup-Kupershmidt equation Fordy-Gibbons equation 

MSC2010 numbers

12D10 35Q51 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Department of Applied MathematicsNational Research Nuclear University “MEPhI”MoscowRussian Federation

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