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

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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)

Included in

Mathematics Commons

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