Symmetric vibrations of higher dimensional nonlinear wave equations

DOI10.1007/s00029-022-00761-7zbMath1486.35299OpenAlexW4214512298MaRDI QIDQ832415

Brian Pigott, Nemanja Kosovalić

Publication date: 25 March 2022

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00029-022-00761-7

zbMATH Keywords

Lyapunov-Schmidt reductionperiodic boundary conditionsimplicit function theoremDiophantine equationsymmetric group actionsymmetric Hopf bifurcation

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Periodic solutions to PDEs (35B10) Bifurcations in context of PDEs (35B32) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50) Second-order semilinear hyperbolic equations (35L71)

Related Items (2)

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Cites Work

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• Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions
• Global bifurcation of periodic solutions with symmetry
• Bifurcation theory. An introduction with applications of PDEs
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• Self-excited vibrations for damped and delayed 1-dimensional wave equations
• Quasi-periodic self-excited travelling waves for damped beam equations
• Construction of periodic solutions of nonlinear wave equations in higher dimension
• KAM for reversible derivative wave equations
• Free nonlinear vibrations for a class of two-dimensional plate equations: standing and discrete-rotating waves
• Hopf bifurcation in the presence of symmetry

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