ar X iv : p at t - so l / 9 60 80 01 v 1 5 A ug 1 99 6 Vortex – Kink Interaction and Capillary Waves in a Vector Superfluid

Interaction of a vortex in a circularly polarized superfluid component of a 2d complex vector field with the phase boundary between superfluid phases with opposite signs of polarization leads to a resonant excitation of a " capillary " wave on the boundary. This leads to energy losses by the vortex–image pair that has to cause its eventual annihilation. 1 Introduction. Several recent publications considered dynamics of a 2d complex vector field, that can be related both to transverse nonlinear optical patterns in polarized light [1, 2, 3] and to the motion of a hypothetical fermionic superfluid [4]. Although dissi-pation may be non-negligible in optical systems, radiation and dispersion effects play there a primary role. In a scalar case, " acoustic " radiation is the principal mechanism of relaxation to lower energy states. In the vector field, that can be interpreted as a combination of two either miscible or immiscible superfluids, a new relaxation mechanism may appear: radiation of capillary waves. In this communication, we explore the influence of this effect on the interaction of a vortex with an interface between two immiscible superfuids. Conservative Galilean dynamics of a 2d complex vector field is described by an evolution equation derived from the Hamiltonian H (see [2]):