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  • Real-valued algebro-geometric solutions of the two-component Camassa-Holm hierarchy
    Eckhardt, Jonathan ...
    We provide a construction of the two-component Camassa-Holm (CH-2) hierarchy employing a new zero-curvature formalism and identify and describe in detail the isospectral set associated to all ... real-valued, smooth, and bounded algebro-geometric solutions of the $n$th equation of the stationary CH-2 hierarchy as the real ▫$n$▫-dimensional torus ▫$\mathbb{T}^n$▫. We employ Dubrovin-type equations for auxiliary divisors and certain aspects of direct and inverse spectral theory for self-adjoint singular Hamiltonian systems. In particular, we employ Weyl-Titchmarsh theory for singular (canonical) Hamiltonian systems. While we focus primarily on the case of stationary algebro-geometric CH-2 solutions, we note that the time-dependent case subordinates to the stationary one with respect to isospectral torus questions.
    Source: Annales de l'Institut Fourier. - ISSN 0373-0956 (Vol. 67, no. 3, 2017, str. 1185-1230)
    Type of material - article, component part ; adult, serious
    Publish date - 2017
    Language - english
    COBISS.SI-ID - 18210905

source: Annales de l'Institut Fourier. - ISSN 0373-0956 (Vol. 67, no. 3, 2017, str. 1185-1230)

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