Integrable string models with constant torsion in terms of chiral invariants of SU(n), SO(n), SP(n groups

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 Riemann space of the chiral primitive invariant currents and on the chiral nonprimitive Casimir operators as Hamiltonians.