I.V. Barashenkov and D.E. Pelinovsky

Exact vortex solutions of the complex sine-Gordon theory on the plane

Phys. Lett. B 436, 117-124 (1998)

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.

Keywords:
INTEGRABLE RELATIVISTIC EQUATIONS, SOLITON SOLUTIONS, NONVANISHING BACKGROUNDS, MODELS