Multi-Soliton solutions to a model equation for shallow water waves

Authors

Zhijiang Qiao, University of Texas-Pan American

Date of Award

8-2010

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Baofeng Feng

Second Advisor

Dr. Paul Bracken

Third Advisor

Dr. Kenichi Maruno

Abstract

In Soliton theory, Hirota direct method is most efficient tool for seeking one soliton solutions or multi-soliton solutions of integrable nonlinear partial differential equations. The key step of the Hirota direct method is to transform the given equation into its Hirota bilinear form. Once the bilinear form of the given equation is found, we can construct the soliton and multi-soliton solutions of that model. Many interesting characteristics of Pfaffians were discovered through studies of soliton equations. In this thesis, a shallow water wave model and its bilinear equation are investigated. Using Hirota direct method, we obtain the multi-soliton solutions and Pfaffian solutions for a shallow water wave model.

Comments

Copyright 2010 Zhijiang Qiao. All Rights Reserved.

https://www.proquest.com/dissertations-theses/multi-soliton-solutions-model-equation-shallow/docview/760046387/se-2?accountid=7119

Granting Institution

University of Texas-Pan American