A normal form for beam and non-local nonlinear Schrödinger equations

DOI10.1088/1751-8113/43/43/434028zbMath1235.37026OpenAlexW2097157928MaRDI QIDQ3057442

Michela Procesi

Publication date: 24 November 2010

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/2b85467787f86a91b4a4e9126d16a1596d89203e

zbMATH Keywords

Hamiltonian PDEquasi-periodic solutionsKAM theory

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

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KAM theory for the reversible perturbations of 2D linear beam equations ⋮ An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation ⋮ Quasi-periodic solutions for quintic completely resonant derivative beam equations on T2 ⋮ Quasi-periodically forced and reversible vibrations of beam equations with Liouvillean frequencies ⋮ Quasi-periodic solution of nonlinear beam equation on \(\mathbb{T}^d\) with forced frequencies ⋮ KAM tori for completely resonant Hamiltonian derivative beam equations on \(\mathbb{T}^2\) ⋮ A KAM algorithm for the resonant non-linear Schrödinger equation ⋮ A normal form for the Schrödinger equation with analytic non-linearities ⋮ Quasi-periodic solutions for a completely resonant beam equation with a nonlinear term depending on the time and space variables ⋮ Chaotic-like transfers of energy in Hamiltonian PDEs ⋮ Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs ⋮ Invariant tori for a two-dimensional completely resonant beam equation with a quintic nonlinear term ⋮ KAM tori for a two dimensional beam equation with a quintic nonlinear term and quasi-periodic forcing

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