A class of nonlinear, completely integrable abstract wave equations

DOI10.1007/BF01063738zbMath0783.35003MaRDI QIDQ1209577

Alain Haraux, Thierry Cazenave, Fred B. Weissler

Publication date: 16 May 1993

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

zbMATH Keywords

Sobolev spacesconservation lawsquasiperiodicityexistence of global, bounded solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Almost and pseudo-almost periodic solutions to PDEs (35B15) Hyperbolic conservation laws (35L65) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (7)

Asymptotic finite-dimensional approximations for a class of extensible elastic systems ⋮ Remarks on weak stabilization of semilinear wave equations ⋮ Long-time behavior of partially damped systems modeling degenerate plates with piers ⋮ Detailed asymptotics for a convex Hamiltonian system with two degrees of freedom ⋮ The role of boundary conditions in the torsional instability of suspension bridges ⋮ A class of nonlinear hyperbolic problems with global solutions ⋮ Chaos and integrability in a nonlinear wave equation

Cites Work

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• Nonlinear effects in the wave equation with a cubic restoring force
• Some oscillatory properties of the wave equation in several space dimensions
• Mouvements presque-périodiques d'une corde vibrante en presence d'un obstacle fixe, rectiligne ou ponctuel
• Detailed asymptotics for a convex Hamiltonian system with two degrees of freedom
• Oscillatory Phenomena Associated to Semilinear Wave Equations in One Spatial Dimension
• Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz
• Periodic solutions of hamiltonian systems

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