Theses and Dissertations - UTB/UTPA

Date of Award


Document Type


Degree Name

Master of Science (MS)



First Advisor

Dr. Barnabas Bede

Second Advisor

Dr. Paul Bracken

Third Advisor

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.


Copyright 2011 Wei Yin. All Rights Reserved.

Granting Institution

University of Texas-Pan American

Included in

Mathematics Commons