Asymptotic stability of $N$-solitons in the cubic NLS equation

Abstract

In this article we consider the Cauchy problem for the cubic focusing nonlinear Schrö\-dinger (NLS) equation on the line with initial datum close to a particular $N$-soliton. Using inverse scattering and the $\bar{\partial }$ method we establish the decay of the $L^{\infty }$ norm of the residual term in time.

26 pages