A note on the construction of Sobolev almost periodic invariant tori for the 1d NLS

DOI10.4171/RLM/923zbMath1473.37091arXiv2009.04312OpenAlexW3130819312MaRDI QIDQ2039135

Luca Biasco, Jessica Elisa Massetti, Michela Procesi

Publication date: 2 July 2021

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.04312

zbMATH Keywords

nonlinear Schrödinger equationalmost periodic solutions

Mathematics Subject Classification ID

Almost and pseudo-almost periodic solutions to PDEs (35B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

Related Items (3)

Small amplitude weak almost periodic solutions for the 1d NLS ⋮ Sub-exponential stability for the beam equation ⋮ Almost-periodic response solutions for a forced quasi-linear Airy equation

Cites Work

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• KAM for autonomous quasi-linear perturbations of mKdV
• Birkhoff normal form for partial differential equations with tame modulus
• Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation
• Quasi-periodic solutions with Sobolev regularity of NLS on \(\mathbb T^d\) with a multiplicative potential
• Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation
• An abstract Birkhoff normal form theorem and exponential type stability of the 1d NLS
• A Nekhoroshev type theorem for the derivative nonlinear Schrödinger equation
• Almost periodic solutions of one dimensional Schrödinger equation with the external parameters
• A normal form à la Moser for diffeomorphisms and a generalization of Rüssmann's translated curve theorem to higher dimensions
• A Nekhoroshev-type theorem for the nonlinear Schrödinger equation on the torus
• On invariant tori of full dimension for 1D periodic NLS
• A Nash-Moser Approach to KAM Theory
• Newton's method and periodic solutions of nonlinear wave equations
• On the construction of almost periodic solutions for a nonlinear Schrödinger equation
• Finite dimensional invariant KAM tori for tame vector fields
• Normal forms for perturbations of systems possessing a Diophantine invariant torus

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