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

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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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
\Bibitem{KotKhr86} \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
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
3. Anders, I, “Asymptotic solitons of the Johnson equation”, Journal of Nonlinear Mathematical Physics, 7:3 (2000), 284
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
5. Anders, I, “Soliton asymptotics of nondecaying solutions of the modified Kadomtsev-Petviashvili-I equation”, Journal of Mathematical Physics, 42:8 (2001), 3673
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
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
8. A. Minakov, “Asymptotics of rarefaction wave solution to the mKdV equation”, Zhurn. matem. fiz., anal., geom., 7:1 (2011), 59–86
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
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
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
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
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