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. DeminaEmail author
  • Nikolai A. Kudryashov


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.


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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