Interior inverse problem for global conservative multipeakon solutions of the Camassa-Holm equation

We consider the interior inverse problem associated with the global conservative multipeakon solution of the Camassa-Holm equation. Based on the inverse spectral theory on the half-line and the oscillation property of eigenfunctions, some (non)uniqueness results of the interior inverse problem are o...

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Bibliographic Details
Published in:Journal of Differential Equations 2024-06, Vol.395, p.262-307
Main Authors: Liu, Tao, Lyu, Kang
Format: Article
Language:English
Subjects:
Interior inverse problem
The Camassa-Holm equation
Weyl-Titchmarsh function
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Summary:We consider the interior inverse problem associated with the global conservative multipeakon solution of the Camassa-Holm equation. Based on the inverse spectral theory on the half-line and the oscillation property of eigenfunctions, some (non)uniqueness results of the interior inverse problem are obtained. In addition, we give the trace formula, which connects the global conservative multipeakon solution with the corresponding eigenvalues and normalized eigenfunctions.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2024.03.018