2016, Heil, Konstantin, Moroianu, Andrei, Semmelmann, Uwe

We show that Killing tensors on conformally at n-dimensional tori whose con- formal factor only depends on one variable, are polynomials in the metric and in the Killing vector elds. In other words, every rst integral of the geodesic ow polynomial in the momenta on the sphere bundle of such a torus is linear in the momenta.

2006, Pietrzyk, Monika, Kanattsikov, I., Bandelow, Uwe

A two component vector generalization of the Schäfer-Wayne short pulse equation which 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 is presented. As a special case, the integrable two-component short pulse equations are constructed which represent the counterpart of the Manakov system in the case of ultra-short pulses.