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

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.

Part of a talk given at a conference on "Nonlinear Physics. Theory and Experiment", Gallipoli (Lecce), June-July 2004. To appear in a topical issue of "Theoretical and Mathematical Physics". 7 pages, 1 figure

References in corpus (1)

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

Cited by in corpus (4)

• Vortices and Polynomials
• Rational solutions of the Boussinesq equation and applications to rogue waves
• The Sasa--Satsuma (complex mKdV II) and the complex sine-Gordon II equation revisited: recursion operators, nonlocal symmetries, and more
• A Constructive Proof for the Umemura Polynomials of the Third Painlevé Equation