Keywords
Bifurcation theory, Differential equations, Nonlinear, Differential equations, Partial, Nonlinear theories, Solitons
Abstract
In this Ph.D. thesis, we study regular and embedded solitons and generalized and degenerate Hopf bifurcations. These two areas of work are seperate and independent from each other. First, variational methods are employed to generate families of both regular and embedded solitary wave solutions for a generalized Pochhammer PDE and a generalized microstructure PDE that are currently of great interest. The technique for obtaining the embedded solitons incorporates several recent generalizations of the usual variational technique and is thus topical in itself. One unusual feature of the solitary waves derived here is that we are able to obtain them in analytical form (within the family of the trial functions). Thus, the residual is calculated, showing the accuracy of the resulting solitary waves. Given the importance of solitary wave solutions in wave dynamics and information propagation in nonlinear PDEs, as well as the fact that only the parameter regimes for the existence of solitary waves had previously been analyzed for the microstructure PDE considered here, the results obtained here are both new and timely.
Notes
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Graduation Date
2011
Semester
Spring
Advisor
Choudhury, S. Roy
Degree
Doctor of Philosophy (Ph.D.)
College
College of Sciences
Department
Mathematics
Format
application/pdf
Identifier
CFE0003634
URL
http://purl.fcla.edu/fcla/etd/CFE0003634
Language
English
Length of Campus-only Access
None
Access Status
Doctoral Dissertation (Open Access)
Subjects
Dissertations, Academic -- Sciences, Sciences -- Dissertations, Academic
STARS Citation
Smith, Todd Blanton, "Variational Embedded Solitons, And Traveling Wavetrains Generated By Generalized Hopf Bifurcations, In Some Nlpde Systems" (2011). Electronic Theses and Dissertations. 1972.
https://stars.library.ucf.edu/etd/1972