On the propagation of vector ultra-short pulses

A two component vector generalization of the Schäfer-Wayne short pulse equation is derived.It describes propagation of ultra-short pulses in optical fibers with Kerr nonlinearity beyond the slowly varying envelope approximation and takes into account the effects of anisotropy and polarization.We show that in a special case this system gives rise to three different integrable two-component short pulse equations which represent the counterpart of the Manakov system in the case of ultra-short pulses.