Date: Tuesday, January 15, 2013
Location: 3866 East Hall (2:10 PM to 3:00 PM)
Title: What is the inversescattering transform?
Abstract: The inversescattering transform was first discovered in the 1960's by Gardner, Greene, Kruskal, and Miura as a method of solving the initialvalue problem for the Kortewegde Vries equation, a wellknown nonlinear partial differential equation modeling (among many other things) the propagation of surface water waves in a channel. It soon became apparent that the method applies more broadly to a wider class of problems of great interest in nonlinear wave theory. I will describe some of the history and then explain how the method can be used to solve the defocusing cubic nonlinear Schr\"odinger equation, as was first discovered by Zakharov and Shabat. As suggested by the name of the method, the key ideas come from the mathematical treatment of the direct and inversescattering problems for various linear equations, problems that are of independent interest in applications (see John Schotland's upcoming talk in this seminar). <br />
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Although this will be Part II, with particular emphasis on the representation of the inverse scattering problem as a RiemannHilbert problem of complex function theory, I will try to make the talk selfcontained for those interested people who may have missed Part I last November.
Files:
Speaker: Peter Miller
Institution: Univ of Michigan
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