Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2011-12-20
Regular and Chaotic Dynamics, 2011, vol 16, No. 6, pp 562-576
Nonlinear Sciences
Exactly Solvable and Integrable Systems
23 pages, 8 figures
Scientific paper
10.1134/S1560354711060025
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.
Demina Maria V.
Kudryashov Nikolay A.
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