Exponential and sub-exponential stability times for the NLS on the circle

DOI10.4171/RLM/850zbMath1432.37095OpenAlexW2951352588WikidataQ115481566 ScholiaQ115481566MaRDI QIDQ2319589

Luca Biasco, Jessica Elisa Massett, Michela Procesi

Publication date: 20 August 2019

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://doi.org/10.4171/rlm/850

zbMATH Keywords

nonlinear Schrödinger equationBirkhoff normal formalmost global existence

Mathematics Subject Classification ID

Almost and pseudo-almost periodic solutions to PDEs (35B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

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An abstract Birkhoff normal form theorem and exponential type stability of the 1d NLS ⋮ Almost global existence for some Hamiltonian PDEs with small Cauchy data on general tori ⋮ Sub-exponential stability for the beam equation

Cites Work

• Unnamed Item
• Growth of Sobolev norms for the analytic NLS on \(\mathbb{T}^2\)
• Resonant dynamics for the quintic nonlinear Schrödinger equation
• Birkhoff normal form for partial differential equations with tame modulus
• Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation
• Nekhoroshev theorem for small amplitude solutions in nonlinear Schrödinger equations
• Superexponential stability of KAM tori.
• A Nekhoroshev type theorem of higher dimensional nonlinear Schrödinger equations
• A Nekhoroshev-type theorem for Hamiltonian systems with infinitely many degrees of freedom
• Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations
• KAM for beating solutions of the quintic NLS
• Growth of Sobolev norms in the cubic defocusing nonlinear Schrödinger equation
• Growth of Sobolev norms in the cubic nonlinear Schrödinger equation with a convolution potential
• A Nekhoroshev-type theorem for the nonlinear Schrödinger equation on the torus
• Long-time instability and unbounded Sobolev orbits for some periodic nonlinear Schrödinger equations
• Sobolev Stability of Plane Wave Solutions to the Cubic Nonlinear Schrödinger Equation on a Torus
• On long time stability in Hamiltonian perturbations of non-resonant linear PDEs
• Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds