Global existence for the defocusing nonlinear Schr\"odinger equations with limit periodic initial data

TL;DR

This paper proves the global existence of solutions to the defocusing nonlinear Schrödinger equation on the real line when initial data are limit periodic functions, expanding understanding of NLS behavior with almost periodic initial conditions.

Contribution

It establishes the global well-posedness of NLS with limit periodic initial data, a class of almost periodic functions, under certain regularity assumptions.

Findings

Global existence of solutions for NLS with limit periodic initial data

Extension of well-posedness results to almost periodic functions

Provides a framework for analyzing NLS with non-decaying initial data

Abstract

We consider the Cauchy problem for the defocusing nonlinear Schr\"odinger equations (NLS) on the real line with a special subclass of almost periodic functions as initial data. In particular, we prove global existence of solutions to NLS with limit periodic functions as initial data under some regularity assumption.