On the spatial asymptotics of solutions of the Ablowitz-Ladik hierarchy

TL;DR

This paper investigates the long-term behavior of solutions to the Ablowitz-Ladik hierarchy, showing that decaying solutions have time-independent leading asymptotics and that solutions close initially remain close over time.

Contribution

It establishes the time independence of the leading asymptotic term and stability of solutions for the Ablowitz-Ladik hierarchy, extending results to the entire hierarchy.

Findings

Leading asymptotic term is time independent for decaying solutions.

Solutions that are initially close remain close over time.

Results apply to the entire Ablowitz-Ladik hierarchy.

Abstract

We show that for decaying solutions of the Ablowitz-Ladik system, the leading asymptotic term is time independent. In addition, two arbitrary bounded solutions of the Ablowitz-Ladik system which are asymptotically close at the initial time stay close. All results are also derived for the associated hierarchy.