An isospectral problem for global conservative multi-peakon solutions of the Camassa-Holm equation

TL;DR

This paper introduces a new isospectral problem for multi-peakon solutions of the Camassa-Holm equation, demonstrating its integrability via inverse spectral transform using Krein and Langer's moment problem solution.

Contribution

It presents a generalized isospectral problem for multi-peakon solutions, extending the understanding of the Camassa-Holm equation's integrability.

Findings

Establishes a generalized isospectral problem for multi-peakon solutions.

Shows the Camassa-Holm equation is integrable via inverse spectral transform.

Utilizes Krein and Langer's indefinite moment problem solution.

Abstract

We introduce a generalized isospectral problem for global conservative multi-peakon solutions of the Camassa-Holm equation. Utilizing the solution of the indefinite moment problem given by M. G. Krein and H. Langer, we show that the conservative Camassa-Holm equation is integrable by the inverse spectral transform in the multi-peakon case.