Mobility of spiral waves

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Abstract
We consider interacting rotating spiral waves (vortices) under conditions when the asymptotic wave number is small and apply consistent approximations near the vortex core and in the outer region and asymptotic matching to derive a mobility relationship that connects the propagation velocity of a vortex with relevant characteristics of the extrinsic phase field in its vicinity. The results are applied to the problem of the existence of bound states of a pair of interacting vortices of the opposite charge. It is found that interaction decays exponentially with separation and remains attractive at all distances.