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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 144, Number 2, Pages 405–409
DOI: https://doi.org/10.4213/tmf1865 (Mi tmf1865) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Complex Sine-Gordon-2: A New Algorithm for Multivortex Solutions on the Plane

N. Olver, I. V. Barashenkov

University of Cape Town
Full-text PDF (167 kB) Citations (9)
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DOI: https://doi.org/10.4213/tmf1865
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 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, complex sine-Gordon equation.
English version:
Theoretical and Mathematical Physics, 2005, Volume 144, Issue 2, Pages 1223–1226
DOI: https://doi.org/10.1007/s11232-005-0153-3
Bibliographic databases:
Language: Russian
Citation: N. Olver, I. V. Barashenkov, “Complex Sine-Gordon-2: A New Algorithm for Multivortex Solutions on the Plane”, TMF, 144:2 (2005), 405–409; Theoret. and Math. Phys., 144:2 (2005), 1223–1226
Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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Linking options:
  • https://www.mathnet.ru/eng/tmf1865
  • https://doi.org/10.4213/tmf1865
  • https://www.mathnet.ru/eng/tmf/v144/i2/p405
    • This publication is cited in the following 9 articles:
    1. Peter A. Clarkson, Chun-Kong Law, Chia-Hua Lin, “A Constructive Proof for the Umemura Polynomials of the Third Painlevé Equation”, SIGMA, 19 (2023), 080, 20 pp.  mathnet  crossref
    2. Zhou Yu., Manukure S., “Rational and Interactive Solutions to the B-Type Kadomtsev-Petviashvili Equation”, J. Appl. Anal. Comput., 11:5 (2021), 2473–2490  crossref  mathscinet  isi
    3. Clarkson P.A. Gomez-Ullate D. Grandati Y. Milson R., “Cyclic Maya Diagrams and Rational Solutions of Higher Order Painleve Systems”, Stud. Appl. Math., 144:3 (2020), 357–385  crossref  mathscinet  isi  scopus
    4. Peter A Clarkson, Ellen Dowie, “Rational solutions of the Boussinesq equation and applications to rogue waves”, Transactions of Mathematics and Its Applications, 1:1 (2017)  crossref
    5. Clarkson, PA, “Vortices and Polynomials”, Studies in Applied Mathematics, 123:1 (2009), 37  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Clarkson, PA, “Rational solutions of the classical Boussinesq system”, Nonlinear Analysis-Real World Applications, 10:6 (2009), 3360  crossref  mathscinet  zmath  isi  scopus
    7. Clarkson, PA, “RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION”, Analysis and Applications, 6:4 (2008), 349  crossref  mathscinet  zmath  isi
    8. Sergyeyev A, Demskoi D, “Sasa-Satsuma (complex modified Korteweg-de Vries II) and the complex sine-Gordon II equation revisited: Recursion operators, nonlocal symmetries, and more”, Journal of Mathematical Physics, 48:4 (2007), 042702  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    9. Peter A. Clarkson, “Special Polynomials Associated with Rational Solutions of the Painlevé Equations and Applications to Soliton Equations”, Comput. Methods Funct. Theory, 6:2 (2006), 329  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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