Nonlocal Hamiltonian structures of the kinetic equation for soliton gas under polychromatic reductions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909564579872768 |
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| author | Vergallo, Pierandrea |
| author_facet | Vergallo, Pierandrea |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_16493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlocal Hamiltonian structures of the kinetic equation for soliton gas under polychromatic reductions Vergallo, Pierandrea Mathematical Physics 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. |
| title | Nonlocal Hamiltonian structures of the kinetic equation for soliton gas under polychromatic reductions |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2501.16493 |