On invariant tori of full dimension for 1D periodic NLS
From MaRDI portal
Publication:2577509
DOI10.1016/j.jfa.2004.10.019zbMath1088.35061OpenAlexW2051633894MaRDI QIDQ2577509
Publication date: 22 December 2005
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jfa.2004.10.019
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Periodic solutions to PDEs (35B10) NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)
Related Items (50)
Persistence of invariant tori in infinite-dimensional Hamiltonian systems ⋮ Almost-periodic solutions for a quasi-periodically forced nonlinear Schrödinger equation ⋮ Growth of Sobolev norms for the analytic NLS on \(\mathbb{T}^2\) ⋮ Invariant Cantor manifolds of quasi-periodic solutions for the derivative nonlinear Schrödinger equation ⋮ Almost periodic solutions of one dimensional Schrödinger equation with the external parameters ⋮ Smooth quasi-periodic solutions for the perturbed mKdV equation ⋮ Exponential stability estimate for the derivative nonlinear Schrödinger equation* ⋮ About linearization of infinite-dimensional Hamiltonian systems ⋮ Almost periodic invariant tori for the NLS on the circle ⋮ The existence of full dimensional invariant tori for 1-dimensional nonlinear wave equation ⋮ Almost-periodic solutions of an almost-periodically forced wave equation ⋮ A Nekhoroshev type theorem for the nonlinear wave equation ⋮ An abstract Birkhoff normal form theorem and exponential type stability of the 1d NLS ⋮ Exponential and sub-exponential stability times for the derivative wave equation ⋮ Quasi-periodic solutions for quintic completely resonant derivative beam equations on T2 ⋮ Invariant tori of full dimension for second KdV equations with the external parameters ⋮ Stability and recursive solutions in Hamiltonian PDEs ⋮ Small amplitude weak almost periodic solutions for the 1d NLS ⋮ The existence of almost-periodic solutions for 1-dimensional nonlinear Schrödinger equation with quasi-periodic forcing ⋮ The existence of almost periodic response solutions for superlinear Duffing's equations ⋮ Quasi-periodic solutions for nonlinear Schrödinger equations with Legendre potential ⋮ Sub-exponential stability for the beam equation ⋮ Resonant dynamics for the quintic nonlinear Schrödinger equation ⋮ Ground state of the discrete elliptic operator and its application ⋮ On the Kolmogorov theorem for some infinite-dimensional Hamiltonian systems of short range ⋮ Kolmogorov-Arnold-Moser theorem for nonlinear beam equations with almost-periodic forcing ⋮ KAM for the derivative nonlinear Schrödinger equation with periodic boundary conditions ⋮ The almost-periodic solutions of the weakly coupled pendulum equations ⋮ A KAM theorem for Hamiltonian partial differential equations with unbounded perturbations ⋮ Invariant tori of full dimension for a nonlinear Schrödinger equation ⋮ Dynamics of Klein-Gordon on a compact surface near a homoclinic orbit ⋮ Linear Schrödinger Equation with an Almost Periodic Potential ⋮ KAM tori for quintic nonlinear Schrödinger equations with given potential ⋮ The stability of full dimensional KAM tori for nonlinear Schrödinger equation ⋮ Analytic solutions of nonlinear elliptic equations on rectangular tori ⋮ KAM tori for the derivative quintic nonlinear Schrödinger equation ⋮ A note on the construction of Sobolev almost periodic invariant tori for the 1d NLS ⋮ ON THE EXISTENCE OF FULL DIMENSIONAL KAM TORUS FOR FRACTIONAL NONLINEAR SCHRÖDINGER EQUATION ⋮ A Nekhoroshev type theorem for the derivative nonlinear Schrödinger equation ⋮ Almost-periodic response solutions for a forced quasi-linear Airy equation ⋮ Almost periodic solutions for a class of linear Schrödinger equations with almost periodic forcing ⋮ Almost periodic solutions for a class of higher dimensional Schrödinger equations ⋮ Full dimension tori of Schrödinger equation ⋮ Long time stability result for 1-dimensional nonlinear Schrödinger equation ⋮ Construction of quasi-periodic solutions for the quintic Schrödinger equation on the two-dimensional torus $\mathbb {T}^2$ ⋮ Super-exponential stability estimate for the nonlinear Schrödinger equation ⋮ The existence of full-dimensional invariant tori for an almost-periodically forced nonlinear beam equation ⋮ PERIODIC AND QUASI-PERIODIC SOLUTIONS FOR THE COMPLEX SWIFT-HOHENBERG EQUATION ⋮ KAM tori for generalized Benjamin-Ono equation ⋮ Quasi-periodic solutions for nonlinear wave equation with singular Legendre potential
Cites Work
- Small divisors with spatial structure in infinite dimensional Hamiltonian systems
- Localization in disordered, nonlinear dynamical systems
- On diffusion in high-dimensional Hamiltonian systems and PDE
- Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations
- On the construction of almost periodic solutions for a nonlinear Schrödinger equation
This page was built for publication: On invariant tori of full dimension for 1D periodic NLS
