Theses and Dissertations

Date of Award

7-2019

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Baofeng Feng

Second Advisor

Dr. Andras Balogh

Third Advisor

Dr. Paul Bracken

Abstract

This thesis will delve into the Kadomtsev-Petviashvili equation or KP equation and it's hierarchy. More specifically, the solition theory around it. To do so, we first explore the soliton theory for the Korteweg de-Vries equation or KdV equation by analysing it through the inverse scattering transform method and presenting it's soliton solutions. Second, we will introduce, Hirota's bilinear form, and understand its main idea. Third, introduce Sato Theory, and use it to formulate the KP hierarchy, via using pseudo-differential operators, presenting the lax operator, the dressing operator, Sato’s equation, and the zero curvature equation (Zakharov-Shabat Equation). Fourth, find the general solution and one-soliton solution to the KP hierarchy and perform a 2-reduction and 3-reduction on the KP hierarchy. Finally, use Hirota's bilinear method (direct method) to find the multiple solition solutions for the KP hierarchy.

Comments

Copyright 2019 Adrian Eugenio Torres. All Rights Reserved.

https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/dissertations-theses/reduction-kp-hierarchy/docview/2355976120/se-2?accountid=7119

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