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arXiv · 1112.4804

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

Maria V. Demina·Nikolay A. Kudryashov
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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 Gamma and -2Gamma 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.

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Maria V. Demina, Nikolay A. Kudryashov. 2011-12-20. Point vortices and polynomials of the Sawada-Kotera and Kaup-Kupershmidt equations. https://doi.org/10.1134/s1560354711060025

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