Scattering theory for the Schrödinger-Debye System

Abstract

We study the Schrödinger-Debye system over ${\mathbb{R}}^d$ iu_t+\frac 12Δu=uv,\quad μv_t+v=λ|u|^2 and establish the global existence and scattering of small solutions for initial data in several function spaces in dimensions $d=2,3,4$. Moreover, in dimension $d=1$, we prove a Hayashi-Naumkin modified scattering result.

arXiv comment22 pages