Author ORCID Identifier
Date Available
4-28-2017
Year of Publication
2017
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Mathematics
First Advisor
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
Recommended Citation
Lindgren, Joseph B., "Orbital Stability Results for Soliton Solutions to Nonlinear Schrödinger Equations with External Potentials" (2017). Theses and Dissertations--Mathematics. 46.
https://uknowledge.uky.edu/math_etds/46
Included in
Atomic, Molecular and Optical Physics Commons, Dynamical Systems Commons, Non-linear Dynamics Commons, Partial Differential Equations Commons, Plasma and Beam Physics Commons
