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arXiv · 2501.16493

Nonlocal Hamiltonian structures of the kinetic equation for soliton gas under polychromatic reductions

Pierandrea Vergallo
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Abstract

We deepen the existence of a nonlocal Hamiltonian formalism for the El's kinetic equation for soliton gas under the polychromatic reduction for a class of interaction kernels. The nonlocality presented is related to semi-Riemannian metrics of constant curvature, conformally flat metrics and hypersurfaces in a pseudo-Euclidean space. These results generalise a previous one that Vergallo and Ferapontov obtained with local Hamiltonian operators. Some examples as the Korteweg-de Vries, the Lieb-Liniger and the separable cases are analysed.

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Pierandrea Vergallo. 2025-01-27. Nonlocal Hamiltonian structures of the kinetic equation for soliton gas under polychromatic reductions. https://arxiv.org/abs/2501.16493

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