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TMF, 1989, Volume 80, Number 1, Pages 15–28 (Mi tmf5109)  

This article is cited in 3 scientific papers (total in 3 papers)

Asymptotic solitons of the sine-Gordon equation

V. P. Kotlyarov


Abstract: The large time asymptotics of the solutions of the sine-Gordon equation which tend to zero when $x\to\infty$ and tend to the finite-gap solution of this equation when $x\to-\infty$ are investigated. It is proved that at $t\to\infty$ these solutions split into infinite series of solitons with variable phases. These solitons are generated by the continuous spectrum of the $L$-operator from the corresponding Lax representation.

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English version:
Theoretical and Mathematical Physics, 1989, 80:1, 679–689

Bibliographic databases:

Received: 11.01.1988

Citation: V. P. Kotlyarov, “Asymptotic solitons of the sine-Gordon equation”, TMF, 80:1 (1989), 15–28; Theoret. and Math. Phys., 80:1 (1989), 679–689

Citation in format AMSBIB
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\by V.~P.~Kotlyarov
\paper Asymptotic solitons of~the sine-Gordon equation
\jour TMF
\yr 1989
\vol 80
\issue 1
\pages 15--28
\mathnet{http://mi.mathnet.ru/tmf5109}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1018552}
\transl
\jour Theoret. and Math. Phys.
\yr 1989
\vol 80
\issue 1
\pages 679--689
\crossref{https://doi.org/10.1007/BF01015305}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1989CJ81900002}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Anders, I, “Asymptotic solitons of the Johnson equation”, Journal of Nonlinear Mathematical Physics, 7:3 (2000), 284  crossref  isi
    2. Anders, I, “Soliton asymptotics of nondecaying solutions of the modified Kadomtsev-Petviashvili-I equation”, Journal of Mathematical Physics, 42:8 (2001), 3673  crossref  isi
    3. Kotlyarov V., Minakov A., “Riemann–Hilbert problem to the modified Korteveg-de Vries equation: Long-time dynamics of the steplike initial data”, J Math Phys, 51:9 (2010), 093506  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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