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.

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We show that propagation of ultrashort (few-cycle) pulses in nonlinear Drude metamaterials with both electric and magnetic Kerr nonlinearities is described by coupled generalized Short Pulse Equations. The resulting system of equations generalizes to the case of metamaterials both the Short Pulse Equation and its vector generalizations.

The pulse compression of ultra-short few-cycles ,pulses in nonlinear optical fibers is studied using the multisympolectic integration of the short pulse equation.