|Date: Tuesday, November 13, 2012
Location: 3096 East Hall (2:10 PM to 3:00 PM)
Title: What is ... the inverse-scattering transform?
Abstract: The inverse-scattering transform was first discovered in the 1960's by Gardner, Greene, Kruskal, and Miura as a method of solving the initial-value problem for the Korteweg-de Vries equation, a well-known 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 inverse-scattering problems for various linear equations, problems that are of independent interest in applications (see John Schotland's talk in this seminar early next semester).
Speaker: Peter Miller
Institution: University of Michigan