Point vortices and polynomials of the Sawada-Kotera and Kaup-Kupershmidt equations
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.
Keywordspoint vortices special polynomials generalized K2 hierarchy Sawada-Kotera equation Kaup-Kupershmidt equation Fordy-Gibbons equation
MSC2010 numbers12D10 35Q51
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