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An Isospectral Problem for Global Conservative Multi-Peakon Solutions of the Camassa–Holm Equation

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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.

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Authors and Affiliations

  1. School of Computer Science & Informatics, Cardiff University, Queen’s Buildings, 5 The Parade, Roath, Cardiff, CF24 3AA, Wales, UK

    Jonathan Eckhardt

  2. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria

    Aleksey Kostenko

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  1. Jonathan Eckhardt
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  2. Aleksey Kostenko
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Correspondence to Jonathan Eckhardt.

Additional information

Communicated by P. Deift

Research supported by the Austrian Science Fund (FWF) under Grant No. Y330 and M1309 as well as by the AXA Mittag-Leffler Fellowship Project, funded by the AXA Research Fund.

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Eckhardt, J., Kostenko, A. An Isospectral Problem for Global Conservative Multi-Peakon Solutions of the Camassa–Holm Equation. Commun. Math. Phys. 329, 893–918 (2014). https://doi.org/10.1007/s00220-014-1905-4

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  • DOI: https://doi.org/10.1007/s00220-014-1905-4

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