Jacek Szmigielski
The Camassa-Holm equation–trente ans après: on the interplay between Approximation Theory, Inverse Problems, and non-smooth Solitons
In Memoriam Anatol Odzijewicz
It has been 30 years since the derivation of the shallow water equation with peaked solitons by R. Camassa and D. Holm. The Camassa-Holm equation has become one of the most studied non-linear equations in recent years. This talk reviews the interplay between the mathematics of peakons (non-smooth solitons) and Approximation Theory. I will survey some decisive developments shaping my understanding of peakons and my motivation to study peakon-bearing equations. I will highlight the role of the Padé and Hermite-Padé approximations in the solution of inverse problems intrinsically related to these non-linear wave equations. This talk is partly based on my recent joint work on the beam problem with Richard Beals and peakons with Hans Lundmark and Xiang-ke Chang.
