## Theses and Dissertations--Mathematics

#### Author ORCID Identifier

http://orcid.org/0000-0002-8731-631X

2017

#### Degree Name

Doctor of Philosophy (PhD)

#### Document Type

Doctoral Dissertation

#### College

Arts and Sciences

#### Department

Mathematics

Dr. Peter D. Hislop

#### Abstract

For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method.

For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.

#### Digital Object Identifier (DOI)

https://doi.org/10.13023/ETD.2017.164

COinS