Dynamics of poles with position-dependent strengths and its optical analogues (Q651196)

The paper deals with vortex dynamics generalized in two ways: (i) making the strengths complex and thus allowing, besides vortices, sources and sinks as well as their superpositions; and (ii) allowing the strengths of the poles to vary as functions of position in the plane. The emphasis is put on the second generalization, which is illustrated with a variety of exact solutions with analogues in geometric optics, where the medium-dependent index of refraction is replaced by the position-dependent strength of a pole. Particularly, the analogues of Snell's law and the law of reflection off a mirror are considered. Interesting numerical results are presented.