Complex sine-Gordon-2: a new algorithm for multivortex solutions on the plane
N. Olver, I. V. Barashenkov
Abstract
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 Painlevé-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.
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