Large Time Asymptotics for a Cubic Nonlinear Schrödinger System in One Space Dimension, II

Abstract

This is a sequel to the paper “Large time asymptotics for a cubic nonlinear Schrödinger system in one space dimension” by the same authors. We continue to study the Cauchy problem for the two-component system of cubic nonlinear Schrödinger equations in one space dimension. We provide criteria for large time decay or non-decay in $L^2$ of the small amplitude solutions in terms of the Fourier transforms of the initial data.