|
This article is cited in 18 scientific papers (total in 18 papers)
Point Vortices and Polynomials of the Sawada–Kotera and Kaup–Kupershmidt Equations
Maria V. Demina, Nikolai A. Kudryashov Department of Applied Mathematics, National Research Nuclear University "MEPhI", 31 Kashirskoe Shosse, 115409 Moscow, Russian Federation
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 $-2\Gamma$ 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.
Keywords:
point vortices, special polynomials, generalized $K_2$ hierarchy, Sawada–Kotera equation, Kaup–Kupershmidt equation, Fordy–Gibbons equation.
Received: 02.09.2011 Accepted: 04.11.2011
Citation:
Maria V. Demina, Nikolai A. Kudryashov, “Point Vortices and Polynomials of the Sawada–Kotera and Kaup–Kupershmidt Equations”, Regul. Chaotic Dyn., 16:6 (2011), 562–576
Linking options:
https://www.mathnet.ru/eng/rcd457 https://www.mathnet.ru/eng/rcd/v16/i6/p562
|
Statistics & downloads: |
Abstract page: | 116 |
|