All ETDs from UAB

Advisory Committee Chair

Yulia Karpeshina

Advisory Committee Members

Ryoichi Kawai

Ian Knowles

Boris Kunin

Kabe Moen

Document Type


Date of Award


Degree Name by School

Doctor of Philosophy (PhD) College of Arts and Sciences


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.