Vortices and polynomials: non-uniqueness of the Adler–Moser polynomials for the Tkachenko equation

DOI10.1088/1751-8113/45/19/195205zbMath1245.35016arXiv1112.4350OpenAlexW2060617421MaRDI QIDQ2890765

Maria V. Demina, Nikolay A. Kudryashov

Publication date: 12 June 2012

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.4350

zbMATH Keywords

stationary equilibriaTkachenko equationAdler-Moser polynomialtranslating relative equilibria

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (13)

Point vortex equilibria related to Bessel polynomials ⋮ Multi-particle dynamical systems and polynomials ⋮ Exploring circulations yielding no vortex equilibria ⋮ Relative equilibrium configurations of point vortices on a sphere ⋮ Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials ⋮ Negative Pell equation and stationary configurations of point vortices on the plane ⋮ Polynomial sequences related to point vortex equilibria with three strengths ⋮ Bifurcation of point vortex equilibria: four-vortex translating configurations and five-vortex stationary configurations ⋮ Stationary configurations of point vortices on a cylinder ⋮ Relations satisfied by point vortex equilibria with strength ratio $-2$ ⋮ Point vortices and classical orthogonal polynomials ⋮ Generalized Adler-Moser and Loutsenko polynomials for point vortex equilibria ⋮ Liouville chains: new hybrid vortex equilibria of the two-dimensional Euler equation

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