A KAM result on compact Lie groups

DOI10.1007/s10440-014-9990-0zbMath1317.37094arXiv1411.0293OpenAlexW3098542200WikidataQ115384826 ScholiaQ115384826MaRDI QIDQ2346541

Livia Corsi, Emanuele Haus, Michela Procesi

Publication date: 2 June 2015

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.0293

zbMATH Keywords

nonlinear Schrödinger equationquasi-periodic solutionssmall divisor problem

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Implicit function theorems; global Newton methods on manifolds (58C15)

Related Items (8)

KAM for PDEs ⋮ Long time dynamics of Schrödinger and wave equations on flat tori ⋮ Long time stability of small finite gap solutions of the cubic nonlinear Schrödinger equation on \(\mathbb{T}^2\) ⋮ Quasi-periodic solutions to nonlinear beam equations on compact Lie groups with a multiplicative potential ⋮ Reducibility of Schrödinger equation on a Zoll manifold with unbounded potential ⋮ On time dependent Schrödinger equations: global well-posedness and growth of Sobolev norms ⋮ Quasi-periodic solutions for the forced Kirchhoff equation on $ \newcommand{\m}{\mu} \newcommand{\T}{\mathbb T} \T^d$ ⋮ Finite dimensional invariant KAM tori for tame vector fields

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• KAM for autonomous quasi-linear perturbations of mKdV
• KAM for quasi-linear KdV
• A KAM algorithm for the resonant non-linear Schrödinger equation
• An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation
• Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces
• On reducibility of Schrödinger equations with quasiperiodic in time potentials
• An abstract Nash-Moser theorem with parameters and applications to PDEs
• Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
• KAM for the nonlinear Schrödinger equation
• Absence of diffusion in the Anderson tight binding model for large disorder or low energy
• On elliptic lower dimensional tori in Hamiltonian systems
• Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
• Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
• Quasi-periodic solutions with Sobolev regularity of NLS on \(\mathbb T^d\) with a multiplicative potential
• An abstract Nash-Moser theorem and quasi-periodic solutions for NLW and NLS on compact Lie groups and homogeneous manifolds
• Quasi-periodic solutions for fully nonlinear forced reversible Schrödinger equations
• Convergent series expansions for quasi-periodic motions
• Quasi-Töplitz Functions in KAM Theorem
• Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential
• Newton's method and periodic solutions of nonlinear wave equations
• Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)

This page was built for publication: A KAM result on compact Lie groups