- Alfredo Wetzel
- February 1, 2 PM
- 2866 East Hall
Many of our favorite linear PDEs on the real line can be solved satisfactorily by using the Fourier transform. Of course the Fourier transform method fails in the non-linear case. In addition, since we cannot use superposition, we cannot simply add simple homogeneous solutions of the equation to build a solution of interest. A natural question is whether there exists an analogous solution procedure in the non-linear case. The inverse scattering transform is such a procedure and has been used with much success (and celebration) to equations such as the KdV and Schroedinger, to name two.
In this talk, I will introduce the inverse scattering transform and discuss in what sense this is an analogue to the Fourier transform. As a concrete application, I will also show how the transform is used on the Schroedinger equation on the real line in the reflectionless case. The talk is intended to be intuitive rather than rigorous and anyone who is interested is encouraged to attend.