Exact vortex solutions of the complex sine-Gordon theory on the plane
I. V. Barashenkov, D. E. Pelinovsky
Abstract
We construct explicit multivortex solutions for the first and second complex sine-Gordon equations. The constructed solutions are expressible in terms of the modified Bessel and rational functions, respectively. The vorticity-raising and lowering Backlund transformations are interpreted as the Schlesinger transformations of the fifth Painleve equation.
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