2011/12/01 by Maria V. Demina, Nikolay A. Kudryashov · 23 citations
Mathematics · Physics and Astronomy · #Algebraic number #Difference polynomials #Differential equation #Fractional Differential Equations Solutions #Hierarchy #Integrable system #Jacobi polynomials #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Orthogonal polynomials #Partial differential equation #Pure mathematics #nlin.SI
paper · pdf · doi:10.1134/s1560354711060025
published in Regular and Chaotic Dynamics 16(6), 562-576 (Pleiades Publishing) · 23 pages, 8 figures
openalex publication_date 2011/12/01 · arxiv created 2011/12/20 · arxiv updated 2012/01/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.