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TMF, 1986, Volume 68, Number 2, Pages 172–186 (Mi tmf5168)  

This article is cited in 12 scientific papers (total in 12 papers)

Solitons of the nonlinear Schrödinger equation generated by the continuum

V. P. Kotlyarov, E. Ya. Khruslov


Abstract: A study is made of the large-time asymptotic behavior of the solutions of the nonlinear Schrödinger equation with attraction that tend to zero as $x\to+\infty$ and to a finite-gap solution of the equation as $x\to-\infty$. It is shown that in the region of the leading edge such solutions decay in the limit $t\to\infty$ into an infinite series of solitons with variable phases, the solitons being generated by the continuous spectrum of the operator $L$ of the corresponding Lax pair.

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English version:
Theoretical and Mathematical Physics, 1986, 68:2, 751–761

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Received: 06.05.1985

Citation: V. P. Kotlyarov, E. Ya. Khruslov, “Solitons of the nonlinear Schrödinger equation generated by the continuum”, TMF, 68:2 (1986), 172–186; Theoret. and Math. Phys., 68:2 (1986), 751–761

Citation in format AMSBIB
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\by V.~P.~Kotlyarov, E.~Ya.~Khruslov
\paper Solitons of the nonlinear Schr\"odinger equation generated by the continuum
\jour TMF
\yr 1986
\vol 68
\issue 2
\pages 172--186
\mathnet{http://mi.mathnet.ru/tmf5168}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=871046}
\zmath{https://zbmath.org/?q=an:0621.35092}
\transl
\jour Theoret. and Math. Phys.
\yr 1986
\vol 68
\issue 2
\pages 751--761
\crossref{https://doi.org/10.1007/BF01035537}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1986G528100002}


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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. V. P. Kotlyarov, “Asymptotic solitons of the sine-Gordon equation”, Theoret. and Math. Phys., 80:1 (1989), 679–689  mathnet  crossref  mathscinet  isi
    2. R. F. Bikbaev, R. A. Sharipov, “Asymptotics at $t\to\infty$ of the solution to the Cauchy problem for the Korteweg–de Vries equation in the class of potentials with finite-gap behavior as $x\to\pm\infty$”, Theoret. and Math. Phys., 78:3 (1989), 244–252  mathnet  crossref  mathscinet  zmath  isi
    3. Anders, I, “Asymptotic solitons of the Johnson equation”, Journal of Nonlinear Mathematical Physics, 7:3 (2000), 284  crossref  isi
    4. V. B. Baranetskii, V. P. Kotlyarov, “Asymptotic behavior in the trailing edge domain of the solution of the KdV equation with an initial condition of the “threshold type””, Theoret. and Math. Phys., 126:2 (2001), 175–186  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Anders, I, “Soliton asymptotics of nondecaying solutions of the modified Kadomtsev-Petviashvili-I equation”, Journal of Mathematical Physics, 42:8 (2001), 3673  crossref  isi
    6. Egorova, I, “On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data: I. Schwartz-type perturbations”, Nonlinearity, 22:6 (2009), 1431  crossref  isi
    7. 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
    8. A. Minakov, “Asymptotics of rarefaction wave solution to the mKdV equation”, Zhurn. matem. fiz., anal., geom., 7:1 (2011), 59–86  mathnet  mathscinet  zmath  elib
    9. Minakov A., “Long-time behavior of the solution to the mKdV equation with step-like initial data”, J. Phys. A: Math. Theor., 44:8 (2011), 085206  crossref  isi
    10. Egorova I., Teschl G., “On the Cauchy Problem for the Kortewegde Vries Equation With Steplike Finite-Gap Initial Data II. Perturbations With Finite Moments”, J Anal Math, 115 (2011), 71–101  crossref  isi
    11. V. Kotlyarov, A. Minakov, “Step-initial function to the mKdV equation: hyper-elliptic long-time asymptotics of the solution”, Zhurn. matem. fiz., anal., geom., 8:1 (2012), 38–62  mathnet  mathscinet  zmath
    12. Zhu J. Wang L. Qiao Zh., “Inverse Spectral Transform For the Ragnisco-Tu Equation With Heaviside Initial Condition”, J. Math. Anal. Appl., 474:1 (2019), 452–466  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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