Journal of High Energy Physics

, 2013:113 | Cite as

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

  • Anton Galajinsky
  • Olaf LechtenfeldEmail author


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.


Integrable Equations in Physics Discrete and Finite Symmetries 


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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Laboratory of Mathematical PhysicsTomsk Polytechnic UniversityTomskRussian Federation
  2. 2.Institut für Theoretische Physik und Riemann Center for Geometry and PhysicsLeibniz Universität HannoverHannoverGermany

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