Reducible KAM tori for two-dimensional nonlinear Schrödinger equations with explicit dependence on the spatial variable
DOI10.1016/j.jfa.2022.109430zbMath1490.35416OpenAlexW4213201335MaRDI QIDQ2114131
Jiansheng Geng, Shuaishuai Xue
Publication date: 15 March 2022
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jfa.2022.109430
Smoothness and regularity of solutions to PDEs (35B65) NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Related Items (2)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Energy supercritical nonlinear Schrödinger equations: quasiperiodic solutions
- KAM for autonomous quasi-linear perturbations of mKdV
- 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
- A normal form for the Schrödinger equation with analytic non-linearities
- KAM for the nonlinear beam equation
- Hamiltonian perturbations of infinite-dimensional linear systems with an imaginary spectrum
- An abstract Nash-Moser theorem with parameters and applications to PDEs
- A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces
- Quasi-periodic solutions of completely resonant nonlinear wave equations
- Quasi-periodic solutions in a nonlinear Schrödinger equation
- Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
- 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
- Nearly integrable infinite-dimensional Hamiltonian systems
- On diffusion in high-dimensional Hamiltonian systems and PDE
- 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. I
- A KAM theorem of degenerate infinite dimensional Hamiltonian systems. II
- Quasi-periodic solutions for a nonlinear wave equation
- Quasi-periodic solutions with Sobolev regularity of NLS on \(\mathbb T^d\) with a multiplicative potential
- Time quasi-periodic gravity water waves in finite depth
- An abstract Nash-Moser theorem and quasi-periodic solutions for NLW and NLS on compact Lie groups and homogeneous manifolds
- A KAM theorem for higher dimensional wave equations under nonlocal perturbation
- A KAM theorem for higher dimensional nonlinear Schrödinger equations
- Quasi-periodic solutions of nonlinear random Schrödinger equations
- Long time dynamics of Schrödinger and wave equations on flat tori
- Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential
- KAM tori for higher dimensional beam equations with constant potentials*
- 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)
- On the construction of almost periodic solutions for a nonlinear Schrödinger equation
- The Cauchy problem for nonlinear Schrödinger equation (NLS) with critical nonlinearity
This page was built for publication: Reducible KAM tori for two-dimensional nonlinear Schrödinger equations with explicit dependence on the spatial variable