On the inverse spectral transform for the conservative Camassa-Holm flow

Jonathan Eckhardt, Loughborough.

The Camassa-Holm equation is a nonlinear partial differential equation that models unidirectional wave propagation on shallow water. I will show how this equation can be integrated by means of the inverse spectral transform method. The global conservative solutions obtained in this way form into a train of solitons (peakons) in the long-time limit.