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Regul. Chaotic Dyn., 2011,  16,  6,  562–576 (Mi rcd457)  

7 ( 7 )

Point Vortices and Polynomials of the SawadaKotera and KaupKupershmidt Equations

Maria V. Demina, Nikolai A. Kudryashov

Department of Applied Mathematics, National Research Nuclear University "MEPhI", 31 Kashirskoe Shosse, 115409 Moscow, Russian Federation

: Rational solutions and special polynomials associated with the generalized $K_2$ hierarchy are studied. This hierarchy is related to the SawadaKotera and KaupKupershmidt equations and some other integrable partial differential equations including the FordyGibbons equation. Differentialdifference 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. Differentialdifference relations enabling one to construct these polynomials explicitly are derived. Algebraic relations satisfied by the roots of the polynomials are found.

 : point vortices, special polynomials, generalized $K_2$ hierarchy, SawadaKotera equation, KaupKupershmidt equation, FordyGibbons equation

DOI: https://doi.org/10.1134/S1560354711060025

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MSC: 12D10, 35Q51
: 02.09.2011
:04.11.2011
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: Maria V. Demina, Nikolai A. Kudryashov, “Point Vortices and Polynomials of the SawadaKotera and KaupKupershmidt Equations”, Regul. Chaotic Dyn., 16:6 (2011), 562–576

AMSBIB
\RBibitem{DemKud11}
\by Maria V. Demina, Nikolai A. Kudryashov
\paper Point Vortices and Polynomials of the SawadaKotera and KaupKupershmidt Equations
\jour Regul. Chaotic Dyn.
\yr 2011
\vol 16
\issue 6
\pages 562--576
\mathnet{http://mi.mathnet.ru/rcd457}
\crossref{https://doi.org/10.1134/S1560354711060025}


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  • http://mi.mathnet.ru/rcd457
  • http://mi.mathnet.ru/rus/rcd/v16/i6/p562

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    x:
    1. Maria V. Demina, Nikolai A. Kudryashov, “Relative Equilibrium Configurations of Point Vortices on a Sphere”, Regul. Chaotic Dyn., 18:4 (2013), 344–355  mathnet  crossref  mathscinet  zmath
    2. Nikolay A. Kudryashov, “Higher Painlevé Transcendents as Special Solutions of Some Nonlinear Integrable Hierarchies”, Regul. Chaotic Dyn., 19:1 (2014), 48–63  mathnet  crossref  mathscinet  zmath
    3. Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, “Special Solutions of a High-order Equation for Waves in a Liquid with Gas Bubbles”, Regul. Chaotic Dyn., 19:5 (2014), 576–585  mathnet  crossref  mathscinet  zmath
    4. Kevin A. O'Neil, Nicholas Cox-Steib, “Generalized AdlerMoser and Loutsenko Polynomials for Point Vortex Equilibria”, Regul. Chaotic Dyn., 19:5 (2014), 523–532  mathnet  crossref  mathscinet  zmath
    5. Kevin A. O'Neil, “Point Vortex Equilibria Related to Bessel Polynomials”, Regul. Chaotic Dyn., 21:3 (2016), 249–253  mathnet  crossref  mathscinet
    6. Maria V. Demina, Nikolai A. Kudryashov, “Multi-particle Dynamical Systems and Polynomials”, Regul. Chaotic Dyn., 21:3 (2016), 351–366  mathnet  crossref  mathscinet
    7. Dariya V. Safonova, Maria V. Demina, Nikolai A. Kudryashov, “Stationary Configurations of Point Vortices on a Cylinder”, Regul. Chaotic Dyn., 23:5 (2018), 569–579  mathnet  crossref
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