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Complex sine-Gordon-2: a new algorithm for multivortex solutions on the plane

N. Olver·I. V. Barashenkov
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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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N. Olver, I. V. Barashenkov. 2005-02-21. Complex sine-Gordon-2: a new algorithm for multivortex solutions on the plane. https://doi.org/10.1007/s11232-005-0153-3

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