Jonathan Eckhardt: Inverse spectral theory for strings and the conservative Camassa-Holm flow

Speaker
Jonathan Eckhardy, Loughborough University

Abstract
The Camassa-Holm equation is a nonlinear PDE that models unidirectional wave propagation on shallow water and features solutions with blow-up in finite time. As a completely integrable system, it can be solved in principle by means of inverse spectral theory for an ODE that is of the same form as that of a generalized indefinite string. I will show how this method of solution can be implemented to solve the Camassa-Holm equation for some classes of initial data. This talk is based on joint works with A. Kostenko.