Noncoaxial multivortices in the complex sine-Gordon theory on the plane

Details Noncoaxial multivortices in the complex sine-Gordon theory on the plane Noncoaxial multivortices in the complex sine-Gordon theory on the plane

2002-02-06

arxiv.org/abs/nlin/0202018v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

40 pages, 7 figures in colour

Scientific paper

10.1088/0951-7715/15/6/317

We construct explicit multivortex solutions for the complex sine-Gordon equation (the Lund-Regge model) in two Euclidean dimensions. Unlike the previously found (coaxial) multivortices, the new solutions comprise $n$ single vortices placed at arbitrary positions (but confined within a finite part of the plane.) All multivortices, including the single vortex, have an infinite number of parameters. We also show that, in contrast to the coaxial complex sine-Gordon multivortices, the axially-symmetric solutions of the Ginzburg-Landau model (the stationary Gross-Pitaevskii equation) {\it do not} belong to a broader family of noncoaxial multivortex configurations.

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