Geodesic
Complex Sine-Gordon-2: A New Algorithm for Multivortex Solutions on the Plane
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 405-409

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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 Painleve-V equation to itself and allows constructing the $n$-vortex solution more efficiently than the previously reported transformation comprising a product of $2n$ maps.
Keywords: vortices, Backlund transformations, Painleve-V equation
Mots-clés : complex sine-Gordon equation. 
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     author = {N. Olver and I. V. Barashenkov},
     title = {Complex {Sine-Gordon-2:} {A} {New} {Algorithm} for {Multivortex} {Solutions} on the {Plane}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {405--409},
     publisher = {mathdoc},
     volume = {144},
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N. Olver; I. V. Barashenkov. Complex Sine-Gordon-2: A New Algorithm for Multivortex Solutions on the Plane. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 405-409. http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a17/