The defocusing NLS equation with nonzero background: Large-time asymptotics in the solitonless region

Abstract

We consider the Cauchy problem for the defocusing Schrödinger (NLS) equation with finite density initial dataRecently, for the space-time region |x/(2t)| < 1 without stationary phase points on the jump contour, Cuccagna and Jenkins presented the asymptotic stability of the Nsoliton solutions for the NLS equation by using the ∂ generalization of the nonlinear steepest descent method. Their asymptotic result is the formHowever, for the space-time region |x/(2t)| > 1, there will be two stationary points appearing on the jump contour, the corresponding long-time asymptotics is still unknown. In this paper, for |x/(2t)| > 1, x/t = O(1), we found a different asymptotic