Infinite Energy Quasi-Periodic Solutions to Nonlinear Schrodinger Equations on R

We present a set of smooth infinite energy global solutions (without spatial symmetry) to the non-integrable, nonlinear Schrodinger equations on R. These solutions are space-time quasi-periodic with two frequencies each. Previous results [3, 4], and the generalization [32], are quasi-periodic in time, but periodic in space. This paper generalizes J. Bourgain's [5] semi-algebraic set method to analyze nonlinear PDEs, in the non-compact space quasi-periodic setting on R.