Long-time asymptotics for the defocusing integrable discrete nonlinear Schr\"odinger equation

TL;DR

This paper analyzes the long-time behavior of solutions to the defocusing integrable discrete nonlinear Schrödinger equation, revealing that solutions decay like t^{-1/2} and are characterized by oscillatory terms.

Contribution

It applies the Deift-Zhou nonlinear steepest descent method to derive precise long-time asymptotics for the discrete nonlinear Schrödinger equation.

Findings

Solutions decay as t^{-1/2} over time.

The asymptotic form involves a sum of two oscillatory terms.

The method provides detailed asymptotic descriptions for the equation.

Abstract

We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schr\"odinger equation by means of the Deift-Zhou nonlinear steepest descent method. The leading term is a sum of two terms that oscillate with decay of order $t^{-1/2}$.