Hamiltonian formalism for non-diagonalisable systems of hydrodynamic type
Mathematical Physics
2025-05-12 v1 math.MP
Abstract
We study the system of first order PDEs for pseudo-Riemannian metrics governing the Hamiltonian formalism for systems of hydrodynamic type. In the diagonal setting the integrability conditions ensure the compatibility of this system and, thanks to a classical theorem of Darboux, the existence of a family of solutions depending on functional parameters. In this paper we study the generalisation of this result to a class of non-diagonalisable systems of hydrodynamic type that naturally generalises Tsarev's integrable diagonal systems.
Keywords
Cite
@article{arxiv.2505.06220,
title = {Hamiltonian formalism for non-diagonalisable systems of hydrodynamic type},
author = {Paolo Lorenzoni and Sara Perletti and Karoline van Gemst},
journal= {arXiv preprint arXiv:2505.06220},
year = {2025}
}
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43 pages