Orateur
Description
The aim of this talk is to discuss infinite-peakon solutions to the Camassa-Holm equation on the line, that is, a class of (conservative) low regularity solutions having the form of an infinite superposition of peakons (peaked solitons). Our major tool is the classical moment problem (in the framework of generalized indefinite strings). In particular, we will discuss which solutions are amenable to this approach, determine which part of the solution can be recovered from the moments of the underlying spectral measure and provide explicit formulas.
As an application, our results can be used to investigate the long-time behavior of these solutions. We will demonstrate this by considering several illustrative examples.
The talk is based on joint work with X.-K. Chang (Beijing) and J. Eckhardt (Loughborough).