A Birkhoff-Lewis type theorem for the nonlinear wave equation

DOI10.1007/s00205-009-0240-yzbMath1197.35169OpenAlexW2050294356MaRDI QIDQ982284

Laura Di Gregorio, Luca Biasco

Publication date: 6 July 2010

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-009-0240-y

zbMATH Keywords

semilinear wave equationanalytic functionperiodic solutionanalytic solutionone space dimensioninfinite-dimensional Hamiltonian systemminimal periodCantor like set

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Periodic solutions to PDEs (35B10) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Second-order semilinear hyperbolic equations (35L71)

Related Items

Periodic perturbations of Hamiltonian systems ⋮ An abstract Birkhoff normal form theorem and exponential type stability of the 1d NLS ⋮ Small amplitude periodic solutions in time for one-dimensional nonlinear wave equations ⋮ Branching of Cantor manifolds of elliptic tori and applications to PDEs ⋮ Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces ⋮ KAM for reversible derivative wave equations ⋮ KAM for beating solutions of the quintic NLS ⋮ A reversible Nekhoroshev theorem for persistence of invariant tori in systems with symmetry

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