1306.5238 (Anton Galajinsky et al.)

On two-dimensional integrable models with a cubic or quartic integral of
motion    [PDF]

Anton Galajinsky, Olaf Lechtenfeld

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 several new families of 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.

View original: http://arxiv.org/abs/1306.5238