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

► We extend the point vortex model to include sources and sinks. ► Vortex strengths are also allowed to be functions of position. ► A Noether-type conservation law is proved for such systems. ► Exact solutions with piecewise constant vortex strengths show optical analogies.► Numerical methods employed to study systems with piecewise linear strength functions.