Theses and Dissertations - UTB/UTPA

Date of Award

8-2013

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Kenichi Maruno

Second Advisor

Dr. Beofeng Feng

Third Advisor

Dr. Zhaoshang Feng

Abstract

Several methods have been proposed to approach the topic of integrable systems of nonlinear partial differential equations. One of these methods is called the Lax pair. The Lax pair is a pair of matrices or operators, that depend on time and satisfy the Lax equation. Based on the inverse scattering method introduced by Gardner, Greene, Kruskal and Miura (1967), Peter Lax introduced the Lax pair to derive soliton equations from the Lax equation. This thesis provides with a brief background on soliton theory, inverse scattering theory, and Lax pairs. The details missing in the work published by Ablowitz, Kaup, Newell, and Segur (AKNS) and Ablowitz-Ladik to derive nonlinear evolution equations for the 2 × 2 Zakharov-Shabat continuous and discrete cases are exposited here. The ideas of AKNS and Ablowitz-Ladik are extended to derive nonlinear evolution equations for both 3×3 continuous and discrete cases. Mathematica is used to obtain the nonlinear evolution equations.

Comments

Copyright 2013 Ana Castillo. All Rights Reserved.

https://www.proquest.com/dissertations-theses/lax-pairs-some-nonlinear-equations/docview/1459462103/se-2

Granting Institution

University of Texas-Pan American

Included in

Mathematics Commons

COinS