Advisory Committee Chair
Yulia Karpeshina
Advisory Committee Members
Ryoichi Kawai
Ian Knowles
Boris Kunin
Kabe Moen
Document Type
Dissertation
Date of Award
2022
Degree Name by School
Doctor of Philosophy (PhD) College of Arts and Sciences
Abstract
Over the years, many methods have been used for solving the Gross-Pitaevskii equation which is also known as a nonlinear Schrodinger equation. In this thesis, we study a nonlinear polyharmonic equation with a periodic potential and quasi-periodic boundary conditions in dimensions higher than one. A special case of the equation, in two dimensions, is the Gross-Pitaevskii equation. This thesis aims to find solutions close to combinations of two plane waves at high energy. To start with, we use a technique similar to that known for the linear case. Then, we construct a method of successive approximations. We obtain the desired solutions as the limit of the successive approximation procedure.
Recommended Citation
Duaibes, Arien, "Resonant Solutions to Gross-Pitaevskii Equation With Periodic Potential" (2022). All ETDs from UAB. 187.
https://digitalcommons.library.uab.edu/etd-collection/187
