Flows on the Saskatchewan: a workshop on integrability and inverse problems.

  • Start Date: 04/05/2019
  • End Date: 04/07/2019
Location: 

University of Saskatchewan

Description: 

Wave propagation has come to encompass a vast and deep array of problems in nonlinear PDEs, the prototype of which is waves on a shallow water surface, as described by the Korteweg-de Vries equation. Extraordinary properties of the KdV equations include the existence of solitary wave solutions, known as solitons and multi-solitons. KdV has an associated linear problem encoded by a Lax pair, which allows one to solve KdV through inverse scattering. The discovery in 1993 of nonsmooth solitary waves — peakons — in another shallow water wave equation, the Camassa-Holm equation, fundamentally changed the paradigm of “integrability”. What makes Camassa-Holm peakons and their generalization, due to Calogero and Fran¸coise, even more surprising is the presence of algebraic curves, usually associated to spectra of smooth solutions.

 

The purpose of this 3-day workshop at the University of Saskatcheawn is to discuss new developments in the analysis and geometry of nonlinear PDEs and their inverse problems, focused especially on linearization, Lax integrability, and algebraic geometry in problems involving solutions with discontinuous derivatives. Speakers will be encouraged to provided historicalcontext and “big picture” ideas in order to help younger attendees access the field. There will also be a mini-course on KdV equations and Schr¨odinger operators, with a view to Camassa-Holm integrability, by Jacek Szmigielski (Saskatchewan) on the first day. 

Organizers:

Hans Lundmark, Linkoping University,

Steven Rayan, University of Saskatchewan,

 

Other Information: 

Location: University of Saskatchewan

 

Schedules and Registration: More information will be made available soon.