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Mathematical and Numerical Analysis of Coupled Nonlinear Schrödinger Equations

Essman, Michael Christopher
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.
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Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.
Date
2010-05-13
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Undergraduate Honors Theses
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EssmanMichael2010.pdf
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Advisor
Shi, Junping
Li, Chi-Kwong
Lewis, Robert Michael
May, Justin
Department
Mathematics
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https://scholarworks.wm.edu/handle/internal/12452
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