High frequency bound states in nonlinear Schr¨odinger equations

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.

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

2022

Author dc:creator

• Sadoveanu, Vlad

Contributors dc:contributor

• Kirr, Eduard-Wilhelm
• Laugesen, Richard S
• Tzirakis, Nikolaos
• Zharnitski, Vadim

• NLS
• bound states

Statement dc:rights

• Copyright 2022 Vlad Sadoveanu

Language dc:language

en, eng

Handle dc:identifier

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

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F116093