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 |
|---|---|
| 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
On two-dimensional integrable models with a cubic or quartic integral of motion. / Galajinsky, Anton; Lechtenfeld, Olaf.
In: Journal of High Energy Physics, Vol. 2013, No. 9, 113, 2013.Research output: Contribution to journal › Article
}
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
AN - SCOPUS:84884643621
VL - 2013
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 9
M1 - 113
ER -