Bifurcation of periodic solutions from a ring configuration in the vortex and filament problems

DOI10.1016/j.jde.2012.01.044zbMath1252.37042arXiv1303.6312OpenAlexW2006979108MaRDI QIDQ414830

Jorge Ize, Carlos García-Azpeitia

Publication date: 11 May 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.6312

zbMATH Keywords

global bifurcationring configuration\((n+1)\)-filament\((n+1)\)-vortexequivariant degree theory

Mathematics Subject Classification ID

Degree theory for nonlinear operators (47H11) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40)

Related Items (11)

Braids of the \(N\)-body problem. II: Carousel solutions by cabling central configurations ⋮ Molecular chains interacting by Lennard-Jones and Coulomb forces ⋮ On variational and topological methods in nonlinear difference equations ⋮ Multiple periodic solutions for \(\Gamma\)-symmetric Newtonian systems ⋮ Global continua of periodic solutions of singular first-order Hamiltonian systems of \(N\)-vortex type ⋮ Standing waves in a counter-rotating vortex filament pair ⋮ Bifurcations of multi-vortex configurations in rotating Bose-Einstein condensates ⋮ Standing waves of fixed period for \(n+1\) vortex filaments ⋮ Choreographies in the \(n\)-vortex problem ⋮ Standing waves in near-parallel vortex filaments ⋮ Global bifurcation of travelling waves in discrete nonlinear Schrödinger equations

Cites Work

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• Bifurcations of Relative Equilibria in the N-Body and Kirchhoff Problems
• Simplified equations for the interaction of nearly parallel vortex filaments
• Stability of Relative Equilibria in the Problem of N+1 Vortices
• The \(N\)-vortex problem. Analytical techniques

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