On two-dimensional integrable models with a cubic or quartic integral of motion
Mathematical Physics
2015-06-16 v2 High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
Integrable two-dimensional models which possess an integral of motion cubic or quartic in velocities are governed by a single prepotential, which obeys a nonlinear partial differential equation. Taking into account the latter's invariance under continuous rescalings and a dihedral symmetry, we construct new integrable models with a cubic or quartic integral, each of which involves either one or two continuous parameters. A reducible case related to the two-dimensional wave equation is discussed as well. We conjecture a hidden D_{2n} dihedral symmetry for models with an integral of n-th order in the velocities.
Cite
@article{arxiv.1306.5238,
title = {On two-dimensional integrable models with a cubic or quartic integral of motion},
author = {Anton Galajinsky and Olaf Lechtenfeld},
journal= {arXiv preprint arXiv:1306.5238},
year = {2015}
}
Comments
1+10 pages; v2: structure improved, introduction extended, one ref. added, version published in JHEP