Asymptotic stability and completeness in 2D nonlinear Schrodinger equation

In this thesis we obtained new results on the asymptotic stability of ground states of the nonlinear Schrödinger equation in space dimension two. Under our hypotheses, the result actually shows asymptotic completeness in the regime of small initial data, i.e. any small initial data evolves into a superposition of a solitary wave (ground state) and a radiative part that decays in time.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Skulkhu, Ruth

Contributors dc:contributor

• Kirr, Eduard-Wilhelm
• Bronski, Jared C.
• Zharnitsky, Vadim
• Laugesen, Richard S.

• Mathematics
• Partial Differential Equations
• Schrödinger Equation
• Nonlinear
• Completeness
• Asymptotic Stability

Statement dc:rights

• © 2012 by Ruth J. Skulkhu. All rights reserved.

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/32082

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/32082