In this talk, I will use the Korteweg-de
Vries equation, non-linear Schrodinger equation, and
the sine-Gordon equation as models to explain some
remarkable properties of a certain class of non-linear
wave equations, the so called "soliton equations".
Some relations to differential geometry will be
discussed. I will also use Richard Palais'
3D-XplorMath Visualization Computer Program to help us
"see" some of these properties.