Date of Award:
5-2024
Document Type:
Thesis
Degree Name:
Master of Science (MS)
Department:
Mathematics and Statistics
Committee Chair(s)
Nghiem Nguyen
Committee
Nghiem Nguyen
Committee
James Powell
Committee
Matthew Young
Abstract
A variety of physical phenomena can be modeled by systems of nonlinear, dispersive wave equations. Such examples include the propagation of a wave through a canal, deep ocean waves with small amplitude and long wavelength, and even the propagation of long-crested waves on the surface of lakes. An important task in the study of water wave equations is to determine whether a solution exists. This thesis aims to determine whether there exists solutions that both travel at a constant speed and are periodic for several systems of water wave equations. The work done in this thesis contributes to the subfields of mathematics known as partial differential equations and nonlinear waves, and has potential applications in the study of fluid dynamics.
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8bb6068bd0a33a90499611fd50045ab7
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Daniels, Jacob, "On the Existence of Periodic Traveling-Wave Solutions to Certain Systems of Nonlinear, Dispersive Wave Equations" (2024). All Graduate Theses and Dissertations, Fall 2023 to Present. 161.
https://digitalcommons.usu.edu/etd2023/161
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