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Analytical and Numerical Investigations of the Kudryashov Generalized KdV Equation

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Date Issued:
2018
Abstract/Description:
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.
Title: Analytical and Numerical Investigations of the Kudryashov Generalized KdV Equation.
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Name(s): Hilton, William, Author
Schober, Constance, Committee Chair
Moore, Brian, Committee Member
Choudhury, Sudipto, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2018
Publisher: University of Central Florida
Language(s): English
Abstract/Description: 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.
Identifier: CFE0007754 (IID), ucf:52395 (fedora)
Note(s): 2018-12-01
M.S.
Sciences, Mathematics
Masters
This record was generated from author submitted information.
Subject(s): Nonlinear higher-order partial differential equations -- equipartition -- FPU -- Korteweg-de Vries -- tanh method
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0007754
Restrictions on Access: campus 2020-06-15
Host Institution: UCF

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