University of Illinois Urbana-Champaign

High frequency bound states in nonlinear Schr¨odinger equations

Sadoveanu, Vlad

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https://hdl.handle.net/2142/116093

Description

Title
High frequency bound states in nonlinear Schr¨odinger equations
Author(s)
Sadoveanu, Vlad
Issue Date
2022-07-12
Director of Research (if dissertation) or Advisor (if thesis)
Kirr, Eduard-Wilhelm
Doctoral Committee Chair(s)
Laugesen, Richard S
Committee Member(s)
  • Tzirakis, Nikolaos
  • Zharnitski, Vadim
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • NLS
  • bound states
Abstract
Nonlinear Schr¨odinger Equations (NLS) play an important part in modelling various phenomena in scientific fields such as quantum mechanics, optics or statistical physics. This thesis is an effort to describe the high frequency bound states in NLS with external potential and generic nonlinear term, mainly characterized by its asymptotic behavior near infinity. In particular, we answer questions about the existence and uniqueness of these high frequency bound states, their shape, decay properties and behavior of relevant norms.
Graduation Semester
2022-08
Type of Resource
Thesis
Copyright and License Information
Copyright 2022 Vlad Sadoveanu

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