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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] K. Pohlmeyer, Commun. Math. Phys., 46 (1976), 207 ; F. Lund, T. Regge, Phys. Rev. D, 14 (1976), 1524 ; Б. С. Гетманов, Письма в ЖЭТФ, 25 (1977), 132; A. Neveu, N. Papanicolaou, Commun. Math. Phys., 58 (1978), 31 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR

[2] S. Sciuto, Phys. Lett. B, 90 (1980), 75 ; Б. С. Гетманов, ТМФ, 48 (1981), 13 | DOI | MR | MR

[3] V. A. Fateev, Int. J. Mod. Phys. A, 6 (1991), 2109 ; I. Bakas, Int. J. Mod. Phys. A, 9 (1994), 3443 ; Q-H. Park, Phys. Lett. B, 328 (1994), 329 ; V. A. Brazhnikov, Nucl. Phys. B, 501 (1997), 685 ; I. Bakas, J. Sonnenschein, JHEP, 0212 (2002), 049 ; E-print hep-th/0211257 | DOI | MR | DOI | MR | Zbl | DOI | MR | DOI | MR | Zbl | DOI | MR

[4] I. V. Barashenkov, D. E. Pelinovsky, Phys. Lett. B, 436 (1998), 117 | DOI | MR

[5] I. V. Barashenkov, V. S. Shchesnovich, R. M. Adams, Nonlinearity, 15 (2002), 2121 | DOI | MR

[6] A. S. Fokas, U. Mugan, M. J. Ablowitz, Physica D, 30 (1988), 247 ; V. Gromak, “Bäcklund transformations of Painlevé equations and their applications”, The Painlevé Property. One Century Later (Cargése School, 3–22 June, 1996), CRM Series in Mathematical Physics, ed. R. Conte, Springer, N.Y., 1999, 687 | DOI | MR | Zbl | MR | Zbl