Theses and Dissertations - UTB/UTPA
Date of Award
Master of Science (MS)
Dr. Barnabas Bede
Dr. Paul Bracken
Dr. Virgil U. Pierce
In recent years, ultradiscrete integrable systems, in which both independent and dependent variables are discretized, have attracted much attention. In this thesis, we show how to obtain all line soliton solutions of (2+1)-dimensional ultradiscrete soliton systems from determinant solutions of discrete soliton systems by taking an ultradiscrete limit. Taking an ultradiscrete limit of determinant solutions with non-negativity, we obtain Casorati determinant-like solutions. Starting from Grammian (Gram-type determinant), we obtain another expression of τ-functions, which leads to a perturbed form after the expansion of Grammian. These two different forms are essentially equivalent, i.e., it is possible to transform a form into the other form by a simple combinatorics. In a Casorati determinant-like expression, there is a big advantage of constructing all possible line soliton solutions easily. Using ultradiscrete determinant-like solutions, we study the details of line soliton interactions of the ultradiscrete two-dimensional Toda lattice (2DTL) equation.
University of Texas-Pan American
Copyright 2011 Wei Yin. All Rights Reserved.