2025/01/27 by Pierandrea Vergallo, Vergallo, Pierandrea
Mathematics · Physics and Astronomy · Engineering · #Gas Dynamics and Kinetic Theory #Optical properties and cooling technologies in crystalline materials #Material Science and Thermodynamics
paper · pdf · doi:10.48550/arxiv.2501.16493
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.