A normal form for the Schrödinger equation with analytic non-linearities
From MaRDI portal
Publication:695571
DOI10.1007/s00220-012-1483-2zbMath1277.35318arXiv1012.0446OpenAlexW3101587407MaRDI QIDQ695571
Claudio Procesi, Michela Procesi
Publication date: 21 December 2012
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1012.0446
NLS equations (nonlinear Schrödinger equations) (35Q55) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10)
Related Items (40)
Energy supercritical nonlinear Schrödinger equations: quasiperiodic solutions ⋮ KAM for PDEs ⋮ KAM for autonomous quasi-linear perturbations of mKdV ⋮ Reducible quasi-periodic solutions for the non linear Schrödinger equation ⋮ Quasi-periodic solutions for perturbed generalized KdV equation ⋮ Reducibility of first order linear operators on tori via Moser's theorem ⋮ Growth of Sobolev norms for the analytic NLS on \(\mathbb{T}^2\) ⋮ A KAM theorem for higher dimensional nonlinear Schrödinger equations ⋮ Long time stability of small finite gap solutions of the cubic nonlinear Schrödinger equation on \(\mathbb{T}^2\) ⋮ On the quasi-periodic solutions for generalized Boussinesq equation with higher order nonlinearity ⋮ Birkhoff normal form for the nonlinear Schrödinger equation ⋮ The energy graph of the non-linear Schrödinger equation ⋮ Long time stability of plane wave solutions to Schrödinger equation on Torus ⋮ KAM tori for defocusing modified KDV equation ⋮ An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation ⋮ Reducibility of the quantum harmonic oscillator in \(d\)-dimensions with polynomial time-dependent perturbation ⋮ A KAM algorithm for two-dimensional nonlinear Schrödinger equations with spatial variable ⋮ KAM for quasi-linear KdV ⋮ Time quasi-periodic vortex patches of Euler equation in the plane ⋮ Stability and recursive solutions in Hamiltonian PDEs ⋮ Allowable graphs of the nonlinear Schrödinger equation and their applications ⋮ Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite gap tori for the 2D cubic NLS equation ⋮ Quasi-periodic solution of nonlinear beam equation on \(\mathbb{T}^d\) with forced frequencies ⋮ Invariant tori for two-dimensional nonlinear Schrödinger equations with large forcing terms ⋮ A KAM algorithm for the resonant non-linear Schrödinger equation ⋮ KAM Tori for higher dimensional quintic beam equation ⋮ Quasi-periodic solutions for quasi-linear generalized KdV equations ⋮ A Nekhoroshev type theorem of higher dimensional nonlinear Schrödinger equations ⋮ A KAM theorem for higher dimensional forced nonlinear Schrödinger equations ⋮ A KAM theorem for space-multidimensional Hamiltonian PDEs ⋮ On a separation and irreducibility problem of polynomials arising from the nonlinear Schrödinger equation ⋮ KAM for beating solutions of the quintic NLS ⋮ A note on growth of Sobolev norms near quasiperiodic finite-gap tori for the 2D cubic NLS equation ⋮ KAM for the nonlinear beam equation ⋮ THE ENERGY GRAPH OF THE NONLINEAR SCHRÖDINGER EQUATION, OPEN PROBLEMS ⋮ Quasi-periodic solutions for d-dimensional beam equation with derivative nonlinear perturbation ⋮ Quasi-periodic solutions for Schrödinger equation with derivative nonlinearity (|u|2pu)x ⋮ Quasi-periodic solutions for fully nonlinear forced reversible Schrödinger equations ⋮ Reducible KAM tori for two-dimensional nonlinear Schrödinger equations with explicit dependence on the spatial variable ⋮ Quasi-periodic solutions of PDEs
Cites Work
- Unnamed Item
- Unnamed Item
- An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation
- Birkhoff normal form for partial differential equations with tame modulus
- Quasi-periodic solutions in a nonlinear Schrödinger equation
- Periodic solutions for the Schrödinger equation with nonlocal smoothing nonlinearities in higher dimension
- Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrödinger equation
- Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
- Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
- Periodic solutions for a class of nonlinear partial differential equations in higher dimension
- The number of integral points on arcs and ovals
- Reducibility of quasiperiodic cocycles in linear Lie groups
- A normal form for beam and non-local nonlinear Schrödinger equations
- 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 normal form for the Schrödinger equation with analytic non-linearities
