Date of Award
2-2010
Document type
dissertation
Access Type
Open Access Dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
First Advisor
Panayotis G. Kevrekidis
Second Advisor
Nathaniel Whitaker
Third Advisor
Hans Johnston
Subject Categories
Mathematics | Statistics and Probability
Abstract
The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potentials in 2(+1) dimensions. I will make predictions about these properties based on a discrete lattice model of coupled ordinary differential equations with the appropriate symmetry. The latter has been justified by Wannier function expansions in a so-called tight-binding approximation in the appropriate parametric regime. Numerical results for the full 2(+1)-D continuum model will be qualitatively compared with discrete model predictions as well as with nonlinear optics experiments in optically induced photonic lattices in photorefractive crystals. The predictions are also relevant for BECs (Bose-Einstein Condensates) in optical lattices.
DOI
https://doi.org/10.7275/1264805
Recommended Citation
Law, Kody John Hoffman, "Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials" (2010). Open Access Dissertations. 179.
https://doi.org/10.7275/1264805
https://scholarworks.umass.edu/open_access_dissertations/179