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We used the invariant local chiral currents of principal chiral models forSU(n), SO(n), SP(n) groups to construct new integrable string equations ofhydrodynamic type on the Riemmann space of the chiral primitive invariantcurrents and on the chiral non-primitive Casimir operators as Hamiltonians.

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