Stationary configurations of point vortices and other logarithmic objects in two dimensions

Abstract

A method is given for analytic determination of new stationary configurations of objects with logarithmic pair potentials in two dimensions such as vortices, charges, and screw dislocations. The method is applicable to configurations with arbitrary mixed strengths in the presence of background fields. New stationary and uniformly translating vortex configurations are presented, some of which can be generated from N-soliton solutions of the Korteweg--de Vries equation.