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Analytical and Numerical Investigations of the Kudryashov Generalized KdV Equation
| 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 |
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| 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. |
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| 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 |
