Integrable equations with non-smooth solitons

Authors

Xianqi Li, University of Texas-Pan American

Date of Award

8-2009

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Zhijun Qiao

Second Advisor

Dr. Andras Balogh

Third Advisor

Dr. Paul Bracken

Abstract

In this thesis, we present a class of integrable equations with non-smooth soliton solutions. In particular, we derive the bi-Hamiltonian structure and Lax pair of the equation pt = bux + \[{u2 — u1)p]x,p = u — uxx, which guarantee its integrability. Another interesting integrable equation we study is (=Jff!i)t = 2uux, which is exactly the first member of the negative KdV hierarchy. Through traveling wave setting arid phase step analysis, we obtain non-smooth soliton solutions of these integrable equations under different boundary condition at infinities. These equations were shown to have peaked soliton (peakon), "W/M-shape" peakon or cusped soliton (cuspon) solutions. Furthermore, some other non-smooth soliton equations are also investigated for our future work.

Comments

Copyright 2009 Xianqi Li. All Rights Reserved.

https://www.proquest.com/dissertations-theses/integrable-equations-with-non-smooth-solitons/docview/304668631/se-2

Granting Institution

University of Texas-Pan American