Pre-Hamiltonian operators related to hyperbolic equations of Liouville type
Exactly Solvable and Integrable Systems
2020-02-25 v1
Abstract
This text is devoted to hyperbolic equations admitting differential operators that map any function of one independent variable into a symmetry of the corresponding equation. We use the term `symmetry driver' for such operators and prove that any symmetry driver of the smallest order is pre-Hamiltonian (i.e., the image of the driver is closed with respect to the standard bracket). This allows us to prove that the composition of a symmetry driver with the Fr\'echet derivative of an integral is also pre-Hamiltonian (in a new set of the variables) if both the symmetry driver and the integral have the smallest orders.
Keywords
Cite
@article{arxiv.2002.10442,
title = {Pre-Hamiltonian operators related to hyperbolic equations of Liouville type},
author = {S. Ya. Startsev},
journal= {arXiv preprint arXiv:2002.10442},
year = {2020}
}
Comments
Very preliminary version