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

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.

23 pages, 8 figures

References in corpus (4)

• Vortices and Polynomials
• Equilibrium of charges and differential equations solved by polynomials
• Special polynomials associated with the fourth order analogue to the Painlev'e equations
• Special polynomials associated with the K2 hierarchy

Cited by in corpus (5)

• Generating Functions, Polynomials and Vortices with Alternating Signs in Bose-Einstein Condensates
• Vortices ans Polynomials: Nonuniqueness of the Adler-Moser polynomials for the Tkachenko equation
• Point vortices and classical orthogonal polynomials
• Special solutions of high order equation for waves in liquid with gas bubbles
• Equilibrium of Charges and Differential Equations Solved by Polynomials II