Nonlinear two-dimensional frequency- and temperature-dependent vortex dynamics in a tilted washboard pinning potential

The Langevin equation for a two-dimensional nonlinear guided vortex motion in a tilted cosine pinning potential in the presence of an ac current is exactly solved in terms of a matrix continued fraction at arbitrary value of the Hall effect. The influence of an ac current of arbitrary amplitude and frequency on the dc and ac magnetoresistivity tensors is theoretically considered. Experimental realization of this model in thin-film geometry opens up a possibility for a variety of experimental studies of directed motion of vortices under [dc + ac)- driving simply by measuring longitudinal and transverse voltages.