Operator-valued Camassa–Holm systems and their integrability
نویسندگان
چکیده
Abstract We study a Sturm–Liouville-type operator with operator-valued coefficients and its iso-spectral deformations, related to new two-component Camassa–Holm-type completely integrable dynamical systems. Based on specially devised gradient-holonomic scheme, generalizing the one before developed for studying spectral problem spatially multidimensional Hilbert–Schmidt Hilbert space, we constructed two compatible Poisson structures an infinite hierarchy of commuting each other conservation laws derived Hamiltonian system. The latter makes it possible state under some additional constraints complete integrability, in particular, develop corresponding inverse spectral-type-based method constructing exact solutions.
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ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 2022
ISSN: ['0377-9017', '1573-0530']
DOI: https://doi.org/10.1007/s11005-022-01566-7