Event Archive

In-person Seminar - Avy Soffer - The Asymptotic States of Nonlinear Schrödinger Type equations

Thursday, November 18, 2021 at 01:20pm - 02:20pm

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IN-PERSON
MATHEMATICAL PHYSICS SEMINAR
RUTGERS UNIVERSITY
HILL 705
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Avy Soffer - Rutgers University

  Date/Time/Location
Thursday, November 18th, 1:20pm; Hill 705

Title
"The Asymptotic States of Nonlinear Schrödinger Type equations"

Abstract

I will describe a new approach to scattering theory, which allows the analysis of interaction terms which are linear and time dependent, and nonlinear terms as well. This is based on deriving (exterior) propagation estimates for such equations, which micro-localize the asymptotic states as time goes to infinity. In particular, the free part of the solution concentrates on the propagation set (x=vt), and the localized leftover is characterized in the phase-space as well. The NLS with radial data in three dimensions is considered, and it is shown that besides the free asymptotic wave, in general, the localized part is smooth, and is localized in the region where |x|^2 is less than t. Furthermore, the localized part has a massive core and possibly a halo which maybe a self-similar solution.

This work is joint with Baoping Liu

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Location   Hill Center 705