Integrable string models with constant SU(3) torsion

Abstract

We used the local invariant chiral currents to obtain new integrable string equations for string WZW model type with SU(3) constant torsion. We solved Burgers equation of motion for first invariant current in. terms of Lambert function. We show that string model with SU(n), n > 3 constant torsion does not integrable, because procedure of decomposition of non-primitive invariant chiral currents to primitive currents is the procedure of introduction of infinite-dimensions matrix of second kind constraints in bi-Hamiltonian approach to integrable systems.