# Soliton equations and Differential Geometry

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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.