Nonlinear standing and rotating waves on the sphere

DOI10.1006/jdeq.2000.3791zbMath0973.35031OpenAlexW2172238643MaRDI QIDQ1586118

Stanislaus Maier-Paape, Timothy J. Healey, Christoph Gugg, Hansjoerg Kielhoefer

Publication date: 12 March 2001

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

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3791

zbMATH Keywords

spatio-temporal patternstime-periodic solutionsemi-linear wave equationglobal solution branches in sense of P. Rabinowitz

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Second-order nonlinear hyperbolic equations (35L70) Bifurcations in context of PDEs (35B32) Hyperbolic equations on manifolds (58J45) Group-invariant bifurcation theory in infinite-dimensional spaces (58E09)

Related Items (7)

Global symmetry-breaking bifurcation for the van der Waals-Cahn-Hilliard model on the sphere \(S^2\) ⋮ Standing waves in a counter-rotating vortex filament pair ⋮ Periodic Navier Solutions for the Plate Equation with Non-Monotone Nonlinearities: the Multidimensional Case ⋮ Standing waves of fixed period for \(n+1\) vortex filaments ⋮ Self-excited vibrations for damped and delayed higher dimensional wave equations ⋮ Symmetry-Breaking Global Bifurcation in a Surface Continuum Phase-Field Model for Lipid Bilayer Vesicles ⋮ Free Vibrations in a Wave Equation Modeling MEMS

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• Newton's method and periodic solutions of nonlinear wave equations
• Free nonlinear vibrations for a class of two-dimensional plate equations: standing and discrete-rotating waves
• A bifurcation theorem for potential operators

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