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

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

2005-02-21

arxiv.org/abs/nlin/0502048v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Part of a talk given at a conference on "Nonlinear Physics. Theory and Experiment", Gallipoli (Lecce), June-July 2004. To appe

Scientific paper

10.1007/s11232-005-0153-3

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.

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