Supercritical Nonlinear Schrödinger equations: Quasi-Periodic Solutions

Abstract

We construct time quasi-periodic solutions to the energy supercritical nonlinear Schrödinger equations on the torus in arbitrary dimensions. This introduces a new approach, which could have general applicability.

62 pages; Duke Math. J. (to appear)

References in corpus (3)

• A KAM algorithm for the resonant non--linear Schrödinger equation
• Pure Point Spectrum of the Floquet Hamiltonian for the Quantum Harmonic Oscillator Under Time Quasi- Periodic Perturbations
• Normal Form for the Schrödinger equation with analytic non--linearities

Cited by in corpus (3)

• Quantitative inductive estimates for Green's functions of non-self-adjoint matrices
• Long time stability of small finite gap solutions of the cubic Nonlinear Schrödinger equation on ${\mathbb{T}}^2$
• An infinite dimensional KAM theorem with application to two dimensional completely resonant beam equation