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arXiv · 1709.03847

Scattering theory for the Schrödinger-Debye System

Simão Correia·Filipe Oliveira
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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.

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Simão Correia, Filipe Oliveira. 2017-09-12. Scattering theory for the Schrödinger-Debye System. https://doi.org/10.1088/1361-6544%2Faaba33

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