Darboux integrability for diagonal systems of hydrodynamic type
Differential Geometry
2023-08-09 v2 Mathematical Physics
math.MP
Abstract
We prove that 1) diagonal systems of hydrodynamic type are Darboux integrable if and only if the corresponding systems for commuting flows are Darboux integrable, 2) systems for commuting flows are Darboux integrable if and only if the Laplace transformation sequences terminate, 3) Darboux integrable systems are necessarily semihamiltonian. We give geometric interpretation for Darboux integrability of such systems in terms of congruences of lines and in terms of solution orbits with respect to symmetry subalgebras, discuss known and new examples.
Keywords
Cite
@article{arxiv.2105.14496,
title = {Darboux integrability for diagonal systems of hydrodynamic type},
author = {Sergey I. Agafonov},
journal= {arXiv preprint arXiv:2105.14496},
year = {2023}
}