Colloquia
Peter Miller Abstract
CAM COLLOQUIUM
“Integrable Nonlinear Waves and Singular Asymptotics”
Peter Miller
Department of Mathematics
University of Michigan
Wednesday November 29, 2006
4:00PM in 129 Hayes-Healy Center
*TEA – 3:30PM in Math Lounge – 257 Hayes-Healy*
Abstract:
This talk will be concerned with nonlinear analogues of the classical methods of analysis for exponential integrals that one uses to study singular limits for linear wave propagation problems solved by Fourier transforms. These analogues apply to nonlinear wave problems that may be treated by a nonlinear analogue of the Fourier transform, the "inverse-scattering transform". We will discuss the use of these techniques to study the semiclassical limit for the focusing nonlinear Schr\"odinger (NLS) equation, and we will also mention some recent work on the modified focusing NLS equation (an equation that tries to make up for shortcomings of the focusing NLS equation arising from modulational instability) and the sine-Gordon equation.
