Date: Monday, October 27, 2014
Location: 3096 East Hall (2:30 PM to 3:30 PM)
Title: Inverse Scattering and the Benjamin-Ono equation
Abstract: Many linear PDEs on the real line can be solved satisfactorily, for certain classes of solutions, using the Fourier transform. In the case of nonlinear PDEs or evolution equations, the direct use of the Fourier transform fails due to the loss of the principle of superposition; we expect nonlinear systems to have – in general – nonlinear responses. A natural question to then ask is whether there exists an analogue of the Fourier transform for nonlinear equations. For certain types of nonlinear equations, the Inverse Scattering Transform (IST) is such an analogue. It has been used with much success (and celebration) on the Korteweg-de Vries (KdV) equation, the archetype of IST theory, among many others.
In this talk, I will broadly introduce the IST and discuss in what sense it is a nonlinear analogue of the Fourier transform. To illustrate the procedure, I will also show how the transform is applied to the Benjamin-Ono equation which is a nonlinear evolution equation amenable to IST theory. The talk is intended to be intuitive rather than rigorous and anyone who is interested is encouraged to attend.
Speaker: Alfredo Wetzel