Dissertation
A KLEIN-GORDON EQUATION REVISITED - NEW SOLUTIONS AND A COMPUTATIONAL METHOD
Doctor of Philosophy (PhD), Washington State University
01/2016
Handle:
https://hdl.handle.net/2376/111456
Abstract
The focus of this dissertation is on Klein-Gordon equations with power-law nonlinearities. First, we study the traveling wave solutions and their characteristics of Klein-Gordon equations with polynomial nonlinearities by using the bifurcation method and the qualitative theory of dynamical systems. Based on the differing phase portraits in different regions, we obtain a variety of exact traveling wave solutions such as soliton solutions, kink and antikink solutions, periodic solutions, singular solutions and periodic singular solutions.
We improve some of the general approaches to finding the traveling wave solution of partial differential equations especially with the auxiliary equation method and the subsidiary ordinary differential equation method. We introduce some special solutions for the subsidiary ordinary differential equation and give a Bäcklund transformation that obtains an infinite sequence of solutions. Moreover, a new subsidiary ordinary differential equation is introduced and a corresponding Bäcklund transformation is given.
We show that new solutions can be obtained for our Klein-Gordon equations by using the auxiliary equation method. In addition, we develop a computational method for the Klein-Gordon equation that still preserves an important characteristic of the equation in the discrete form.
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Details
- Title
- A KLEIN-GORDON EQUATION REVISITED - NEW SOLUTIONS AND A COMPUTATIONAL METHOD
- Creators
- Lewa’ Mahmoud Alzaleq
- Contributors
- VALIPURAM S. MANORANJAN (Advisor)MICHAEL TSATSOMEROS (Committee Member)XUEYING WANG (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 249
- Identifiers
- 99900581522101842
- Language
- English
- Resource Type
- Dissertation