Date Thesis Awarded
5-2010
Access Type
Honors Thesis -- Access Restricted On-Campus Only
Degree Name
Bachelors of Science (BS)
Department
Mathematics
Advisor
Junping Shi
Committee Members
Chi-Kwong Li
Robert Michael Lewis
Justin May
Abstract
Radially symmetric solutions of many important systems of partial differential equations can be reduced to systems of special ordinary differential equations. Using methods for determining explicit solutions given certain conditions and assumptions, we find and explore solutions to the one-dimensional Nonlinear Schrödinger problem. Specifically, we find a semi-trivial solution, then find explicit solutions with the methods derived from solving the semi-trivial solutions and from previous work in the field. We also developed a numerical solver for initial value problems for such systems based on Matlab, and we obtain numerical bifurcation diagrams. Various bifurcation diagrams of coupled Schrödinger equations from non-linear physics are obtained, which suggests the uniqueness of the ground state solution.
Recommended Citation
Essman, Michael Christopher, "Mathematical and Numerical Analysis of Coupled Nonlinear Schrödinger Equations" (2010). Undergraduate Honors Theses. William & Mary. Paper 714.
https://scholarworks.wm.edu/honorstheses/714
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Comments
Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.