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

Anton Galajinsky, Olaf Lechtenfeld

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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 nth order in the velocities.

Original languageEnglish
Article number113
JournalJournal of High Energy Physics
Issue number9
Publication statusPublished - 2013



  • Discrete and Finite Symmetries
  • Integrable Equations in Physics

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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