Long-Time Asymptotics for the Defocusing Integrable Discrete Nonlinear Schrödinger Equation II

Abstract

We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation. If |n| < 2t, we have decaying oscillation of order O(t⁻¹/²) as was proved in our previous paper. Near |n|=2t, the behavior is decaying oscillation of order O(t⁻¹/³) and the coefficient of the leading term is expressed by the Painlevé II function. In |n| > 2t, the solution decays more rapidly than any negative power of n.