Abstract
This thesis concerns an analytical and numerical study of the Kudryashov Generalized Korteweg-de Vries (KG KdV) equation. Using a refined perturbation expansion of the Fermi-Pasta-Ulam (FPU) equations of motion, the KG KdV equation, which arises at sixth order, and general higher order KdV equations are derived. Special solutions of the KG KdV equation are derived using the tanh method. A pseudospectral integrator, which can handle stiff equations, is developed for the higher order KdV equations. The numerical experiments indicate that although the higher order equations exhibit complex dynamics, they fail to reach energy equipartition on the time scale considered.
Notes
If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at STARS@ucf.edu
Graduation Date
2018
Semester
Fall
Advisor
Schober, Constance
Degree
Master of Science (M.S.)
College
College of Sciences
Department
Mathematics
Degree Program
Mathematical Science; Industrial Mathematics
Format
application/pdf
Identifier
CFE0007754
URL
http://purl.fcla.edu/fcla/etd/CFE0007754
Language
English
Release Date
6-15-2020
Length of Campus-only Access
1 year
Access Status
Masters Thesis (Open Access)
STARS Citation
Hilton, William, "Analytical and Numerical Investigations of the Kudryashov Generalized KdV Equation" (2018). Electronic Theses and Dissertations. 6606.
https://stars.library.ucf.edu/etd/6606