I will give an overview (or rather my personal point of view) on the topics mentioned in the title. I will start from presenting the Darboux transformations for a few linear operators. Then I will associate nonlinear equations with some of these operators. Finally, I will geometrize selected examples.
Contact A.P. Fordy (email: allan@maths.leeds.ac.uk ) for further details.
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Last updated March 5th, 2007.