Large-time existence results for the nonlocal NLS around ground state solutions

TL;DR

This paper proves that solutions to the nonlocal nonlinear Schrödinger equation stay close to ground state solitons over large times if initially close, using hyperbolic dynamics and stability analysis.

Contribution

It establishes large-time existence results for solutions near ground state solitons in the nonlocal NLS, leveraging hyperbolic dynamics and stability methods.

Findings

Solutions remain close to the soliton orbit over large times

Hyperbolic dynamics near ground state are key to stability

Local structural stability of solutions is demonstrated

Abstract

This paper discusses about solutions of the nonlocal nonlinear Schrodinger equation. We prove that the solution remains close to the orbit of the soliton for a large-time, if the initial data is close to the ground state solitons. The proof uses the hyperbolic dynamics near ground state, which exhibits properties of local structural stability of solutions with respect to the flows of the nonlocal nonlinear Schrodinger equation.