Theses and Dissertations

Date of Award

12-2018

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Zhijun Qiao

Second Advisor

Dr. Andras Balogh

Third Advisor

Dr. Anahit Galstyan

Abstract

In this paper we outline a method for obtaining generalized peakon solutions for a cubic Camassa-Holm model originally introduced by Fokas (1995) and recently shown to have a Lax pair representation and bi-Hamiltonian structure by Qiao et al (2012). By considering an amended signum function—denoted sgn &thetas;(x)—where sgn(0) = &thetas; for a constant &thetas;, we explore new generalized peakon solutions for this model. In this context, all previous peakon solutions are of the case &thetas; = 0. Further, we aim to analyze the algebraic quadratic equation resulting from a substitution of the single-peakon ansatz equipped with our amended signum function in order to determine the effects of constants k1, k2, c, and &thetas; on the wave height. Moreover, we introduce a new measure R relating the scalars k1, k2 of the cubic and quadratic nonlinearity terms which we find has deterministic properties relating to the existence of real vs complex solutions.

Comments

Copyright 2018 Michael Rippe. All Rights Reserved.

https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/dissertations-theses/generalized-amp-thetas-parameter-peakon-solutions/docview/2178344405/se-2?accountid=7119

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