Quasi-periodic solutions for 1D Schrödinger equation with the nonlinearity \(|u|^{2p}u\)
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Publication:926861
DOI10.1016/J.JDE.2008.02.015zbMath1153.35072OpenAlexW2081515230MaRDI QIDQ926861
Publication date: 21 May 2008
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2008.02.015
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)
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Cites Work
- Unnamed Item
- Unnamed Item
- A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces
- Quasi-periodic solutions in a nonlinear Schrödinger equation
- KAM for the nonlinear Schrödinger equation
- Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
- Perturbations of lower dimensional tori for Hamiltonian systems
- Invariant tori for nearly integrable Hamiltonian systems with degeneracy
- KAM tori for 1D nonlinear wave equations with periodic boundary conditions
- Persistence of lower-dimensional tori under the first Melnikov's non-resonance condition
- A KAM theorem for one dimensional Schrödinger equation with periodic boundary conditions
- Construction of periodic solutions of nonlinear wave equations in higher dimension
- Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
- A KAM theorem of degenerate infinite dimensional Hamiltonian systems. II
- A KAM theorem with applications to partial differential equations of higher dimensions
- On long time stability in Hamiltonian perturbations of non-resonant linear PDEs
- Newton's method and periodic solutions of nonlinear wave equations
- Green's Function Estimates for Lattice Schrodinger Operators and Applications. (AM-158)
- Quasi-Periodic Solutions for 1D Schrödinger Equations with Higher Order Nonlinearity
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