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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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Theoretical and Mathematical Physics, 1989, 80:1, 679–689
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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
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\yr 1989
\vol 80
\issue 1
\pages 15--28
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\transl
\jour Theoret. and Math. Phys.
\yr 1989
\vol 80
\issue 1
\pages 679--689
\crossref{https://doi.org/10.1007/BF01015305}
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http://mi.mathnet.ru/eng/tmf5109 http://mi.mathnet.ru/eng/tmf/v80/i1/p15
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This publication is cited in the following articles:
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Anders, I, “Asymptotic solitons of the Johnson equation”, Journal of Nonlinear Mathematical Physics, 7:3 (2000), 284
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Anders, I, “Soliton asymptotics of nondecaying solutions of the modified Kadomtsev-Petviashvili-I equation”, Journal of Mathematical Physics, 42:8 (2001), 3673
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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
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