### 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 nth order in the velocities.

Original language | English |
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Article number | 113 |

Journal | Journal of High Energy Physics |

Volume | 2013 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2013 |

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### Keywords

- Discrete and Finite Symmetries
- Integrable Equations in Physics

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2013*(9), [113]. https://doi.org/10.1007/JHEP09(2013)113

**On two-dimensional integrable models with a cubic or quartic integral of motion.** / Galajinsky, Anton; Lechtenfeld, Olaf.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2013, no. 9, 113. https://doi.org/10.1007/JHEP09(2013)113

}

TY - JOUR

T1 - On two-dimensional integrable models with a cubic or quartic integral of motion

AU - Galajinsky, Anton

AU - Lechtenfeld, Olaf

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Discrete and Finite Symmetries

KW - Integrable Equations in Physics

UR - http://www.scopus.com/inward/record.url?scp=84884643621&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884643621&partnerID=8YFLogxK

U2 - 10.1007/JHEP09(2013)113

DO - 10.1007/JHEP09(2013)113

M3 - Article

VL - 2013

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 9

M1 - 113

ER -