Complex sine-Gordon-2: a new algorithm for multivortex solutions on the   plane
  We present a new vorticity-raising transformation for the second integrable complexification of the sine-Gordon equation on the plane. The new transformation is a product of four Schlesinger maps of the Painlev\'{e}-V to itself, and allows a more efficient construction of the $n$-vortex solution than the previously reported transformation comprising a product of $2n$ maps. 
N. Olver and I.V. Barashenkov