Infinite energy quasi-periodic solutions to nonlinear Schrödinger equations on $\mathbb{R}$

Abstract

We present a set of smooth infinite energy global solutions (without spatial symmetry) to the non-integrable, nonlinear Schrödinger equations on $\mathbb{R}$. These solutions are space-time quasi-periodic with two frequencies each. Previous results [B2,1], and their generalizations [W2-4], are quasi-periodic in time, but periodic in space. This paper generalizes Bourgain's semi-algebraic set method [B3] to analyze nonlinear PDEs, in the non-compact space quasi-periodic setting on $\mathbb{R}$.

to appear in Int. Math. Res. Not

References in corpus (3)

• The nonlinear Schrodinger equation on Z and R with bounded initial data: examples and conjectures
• Quasi-Periodic Solutions For Nonlinear Klein-Gordon Equations
• Space Quasi-Periodic Standing Waves for Nonlinear Schrödinger Equations

Cited by in corpus (1)

• The nonlinear Schrodinger equation on Z and R with bounded initial data: examples and conjectures