NEW CLASS OF RUNNING-WAVE SOLUTIONS OF THE (2+1)-DIMENSIONAL SINE-GORDON EQUATION

A new class of running-wave solutions of the (2 + 1)-dimensional sine-Gordon equation is investigated. The obtained waves require two spatial dimensions for their propagation, i.e. they generalize solutions of the (2 + 0)-dimensional sine-Gordon equation. The parameters of the waves strongly depend on the wave amplitude and there exist forbidden areas for the wavenumber and frequency. The obtained solutions describe a new class of Josephson waves whose velocity is smaller than the Swihart velocity. If omega = 0 the running waves are reduced to the self-consistent phase, current and magnetic field distributions in a large two-dimensional Josephson junction. The self-restriction coefficient for the Josephson current corresponding to one of the structures is calculated.