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

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.

1+10 pages; v2: structure improved, introduction extended, one ref. added, version published in JHEP

References in corpus (3)

• On a class of integrable systems with a quartic first integral
• New families of integrable two-dimensional systems with quartic second integrals
• Explicit integrable systems on two dimensional manifolds with a cubic first integral

Cited by in corpus (4)

• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Superintegrable systems on spaces of constant curvature
• New superintegrable models on spaces of constant curvature
• Integrable Cosmological Potentials