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
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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 -