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SIGMA 4 (2008), 041, 16 pages arXiv:0805.0656
https://doi.org/10.3842/SIGMA.2008.041
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics
Integrable String Models in Terms of Chiral Invariants of SU(n), SO(n), SP(n) Groups
Victor D. Gershun
ITP, NSC Kharkiv Institute of Physics and Technology, Kharkiv, Ukraine
Received October 30, 2007, in final form April 22, 2008; Published online May 06, 2008
Abstract
We considered two types of string models: on the
Riemmann space of string coordinates with null torsion and on the
Riemman-Cartan space of string coordinates with constant torsion.
We used the hydrodynamic approach of Dubrovin, Novikov to
integrable systems and Dubrovin solutions of WDVV associativity
equation to construct new integrable string equations of
hydrodynamic type on the torsionless Riemmann space of chiral
currents in first case.
We used the invariant local chiral currents of principal chiral
models for SU(n), SO(n), SP(n) groups to construct new
integrable string equations of hydrodynamic type on the Riemmann
space of the chiral primitive invariant currents and on the chiral
non-primitive Casimir operators as Hamiltonians in second case.
We also used Pohlmeyer tensor nonlocal currents to construct new
nonlocal string equation.
Key words:
string; integrable models; Poisson brackets; Casimir operators; chiral currents.
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