Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 041, 16 pages      arXiv:0805.0656
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

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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