Thomas Hill, Utah State University
Nonlinear evolution equations are a class of partial differential equations used to model many important physical phenomena such as water waves, transmission of signals in optical fibers, and magnetic fields. In the late 1960Ûªs Zabusky, Kruskal, and others discovered that some special evolution equations, such as the Korteweg-de Vries (KdV), AKNS, nonlinear Schrodinger, and Harry Dym equations, admit localized traveling wave solutions which are stable under interactions. These traveling wave solutions are called solitons. This discovery created a revolution in mathematics that resulted in a new field of study called integrable systems and soliton theory. The goals of my research are the following: provide a database of the most well known integrable systems and their properties; create computational tools to determine if an integrable system has one of the specific properties listed above; and create software that will allow the calculation of one or more of these properties from the others. Building this database and studying these properties in general requires enormous amounts of computation that have done using computer algebra software packages developed at USU by Dr. Ian Anderson.