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Mathematical and Numerical Analysis of Coupled Nonlinear Schrödinger Equations

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Author: Essman, Michael Christopher
Advisor: Shi, Junping
Committee Members: Li, Chi-Kwong; Lewis, Robert Michael; May, Justin
Issued Date: 2010-05-13
URI: http://hdl.handle.net/10288/2011
Description: 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.
Degree: Bachelors of Science in Mathematics

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