The nonlinear Schrodinger equation on Z and R with bounded initial data: examples and conjectures
Analysis of PDEs
2020-05-20 v2 Mathematical Physics
math.MP
Abstract
We study the nonlinear Schr\"odinger equation (NLS) with bounded initial data which does not vanish at infinity. Examples include periodic, quasi-periodic and random initial data. On the lattice we prove that solutions are polynomially bounded in time for any bounded data. In the continuum, local existence is proved for real analytic data by a Newton iteration scheme. Global existence for NLS with a regularized nonlinearity follows by analyzing a local energy norm.
Cite
@article{arxiv.2003.08849,
title = {The nonlinear Schrodinger equation on Z and R with bounded initial data: examples and conjectures},
author = {Benjamin Dodson and Avraham Soffer and Thomas Spencer},
journal= {arXiv preprint arXiv:2003.08849},
year = {2020}
}
Comments
22 pages