Dr. Debnath presented an enlightening lecture on the history of solitons and the roles they play in the area of mathematics and physics. In 1834, John Scott Russell first observed what is today called solitons while observing a boat being drawn along rapidly by a pair of horses. When the boat stopped, he noticed that the bow wave continued forward at great velocity and assumed the form a large solitary elevation. This event was the beginning of many experiments by Mr. Russell who latter in 1844 dubbed the "Wave of Translation". Little was done until the 1960's when scientist began to use modern digital computers to study non-linear wave propagation. As a result of research performed at Los Alamos 1965, an explosion of activity in physics, electronics and biology when it was discovered that many phenomena in theses area could be described through the mathematical and physical theory of the soliton.

Dr. Debnath pointed out that the process of obtaining a solution of linear differential equations is simplified by the use of Fourier transform but that there was no simple method to simplify nonlinear equations. He then pointed out that certain nonlinear differential equations could be fully solved by methods such as KdV (Korteweg-de-Vries) equations, nonlinear Schrodinger, and sine-Gordon equations. He then presented several examples involving KdV equations.

Dr. Debnath concluded his presentation by noting that after the long delay following Scott Russell's observation and research, solitons are now an important area of research in math and physics. Some of the areas for which interest has arisen include fluid dynamics, solid mechanics, optics, acoustics and the list goes on…