Date Thesis Awarded

5-2010

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Junping Shi

Committee Member

Chi-Kwong Li

Committee Member

Robert Michael Lewis

Committee Member

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.

Creative Commons License

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.

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