Radial, vortex, and spiral solutions to the nonlinear Schrödinger equation and other reaction--diffusion systems

This dissertation explores various solutions to nonlinear reaction-diffusion systems, focusing primarily on the nonlinear Schrödinger equation. Three types of solutions are investigated: radial solutions (with no angular dependence), vortex solutions (with angular dependence but no radial phase dependence), and spiral solutions (which have radial phase dependence). The study considers free particles without potential and trapped particles inside the cylindrical potential with an impenetrable barrier. We show that spiral solutions to the nonlinear Schrödinger equation only exist for a radially constant phase by considering a related system of nonlinear ordinary differential equations. This system is shown to be a special case of the $\lambda$-ω reaction-diffusion system, whose spiral solutions exist for a nonconstant phase.

Grantor dc:publisher

University of Tennessee at Chattanooga

Author dc:creator

• Cummins, James Redmon

Contributors dc:contributor

• Cox, Christopher
• Belinskiy, Boris; Nichols, Roger; Kong, Lingju
• College of Engineering and Computer Science

• Differential equations, Nonlinear--Numerical solutions
• Gross-Pitaevskii equations
• Reaction-diffusion equations

Licence

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language

English, eng

Repository record dc:identifier

https://scholar.utc.edu/theses/972

OAI identifier oai:identifier

oai:scholar.utc.edu:theses-2150