University of Illinois Urbana-Champaign

Asymptotic stability and completeness in 2D nonlinear Schrodinger equation

Skulkhu, Ruth

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

Description

Title
Asymptotic stability and completeness in 2D nonlinear Schrodinger equation
Author(s)
Skulkhu, Ruth
Issue Date
2012-06-27T21:32:05Z
Director of Research (if dissertation) or Advisor (if thesis)
Kirr, Eduard-Wilhelm
Doctoral Committee Chair(s)
Bronski, Jared C.
Committee Member(s)
  • Zharnitsky, Vadim
  • Kirr, Eduard-Wilhelm
  • Laugesen, Richard S.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Mathematics
  • Partial Differential Equations
  • Schrödinger Equation
  • Nonlinear
  • Completeness
  • Asymptotic Stability
Abstract
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.
Graduation Semester
2012-05
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http://hdl.handle.net/2142/32082
Copyright and License Information
© 2012 by Ruth J. Skulkhu. All rights reserved.

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