Dissertation
Solitary waves in Fermi-Pasta-Ulam-Tsingou lattices with long range particle interaction
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2024
DOI:
https://doi.org/10.17918/00010698
Abstract
We study the existence and properties of certain kind of traveling waves (nearsonic solitary waves) in Fermi-Pasta-Ulam-Tsingou (FPUT) Lattices. These are infinite, one dimensional chain of identical particles arranged on a horizontal line with infinite nonlocal particle neighbors interactions on both sides. We consider both next neighbor particle interactions and long range particle interactions. In both cases, we prove the existence of localized traveling waves which relies on the Implicit Function Theorem. Techniques of Fourier analysis enable us to reformulate the problem to the study of waves that are small perturbations of well known ODEs. Additionally, we deploy the method originally developed by Beale for a capillary water wave problem to prove the existence of nanopterons solutions. The nanopteron wave profiles are formed by the superposition of an exponentially decaying term (a small perturbation of a KdV sech² -type soliton) and a periodic term with a very small amplitude. The solution develops a ripple as |x| [right arrow] [infinity]. The periodic wave solution is an essential part of our analysis.
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Details
- Title
- Solitary waves in Fermi-Pasta-Ulam-Tsingou lattices with long range particle interaction
- Creators
- Udoh N. Akpan
- Contributors
- Jay Douglas Wright (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- viii, 113 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 991021890114004721