R. F. Bikbaev, “Complex Whitham deformations in the problems with “integrable instability””, TMF, 104:3 (1995), 393–419; Theoret. and Math. Phys., 104:3 (1995), 1078

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Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 104, Number 3, Pages 393–419 (Mi tmf1346)

This article is cited in 13 scientific papers (total in 13 papers)

Complex Whitham deformations in the problems with “integrable instability”

R. F. Bikbaev

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Full-text PDF (2535 kB) Citations (13)

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Abstract: The focusing nonlinear Schrödinger equation with finite-density boundary conditions as

| x | \to \infty

$|x|\!\to \!\infty$ is considered. The asymptotic behavior of the solution as

t \to \infty

$t\!\to \!\infty$ is investigated by means of the complex theory of

ζ

$\zeta$ deformations of Whitham.

Received: 27.10.1994

English version:
Theoretical and Mathematical Physics, 1995, Volume 104, Issue 3, Pages 1078–1097
DOI: https://doi.org/10.1007/BF02068740

Bibliographic databases:

Language: Russian

Citation: R. F. Bikbaev, “Complex Whitham deformations in the problems with “integrable instability””, TMF, 104:3 (1995), 393–419; Theoret. and Math. Phys., 104:3 (1995), 1078–1097

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

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\vol 104

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\pages 1078--1097

\crossref{https://doi.org/10.1007/BF02068740}

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Linking options:

https://www.mathnet.ru/eng/tmf1346

https://www.mathnet.ru/eng/tmf/v104/i3/p393

This publication is cited in the following 13 articles:

Zhaoyu Wang, Meisen Chen, Engui Fan, “Long time asymptotics for the focusing nonlinear Schrödinger equation in the solitonic region with the presence of high-order discrete spectrum”, Journal of Mathematical Analysis and Applications, 505:2 (2022), 125635
Anne Boutet de Monvel, Jonatan Lenells, Dmitry Shepelsky, “The Focusing NLS Equation with Step-Like Oscillating Background: Scenarios of Long-Time Asymptotics”, Commun. Math. Phys., 383:2 (2021), 893
Kotlyarov V., Minakov A., “Dispersive Shock Wave, Generalized Laguerre Polynomials, and Asymptotic Solitons of the Focusing Nonlinear Schrodinger Equation”, J. Math. Phys., 60:12 (2019), 123501
Gino Biondini, Jonathan Lottes, “Nonlinear interactions between solitons and dispersive shocks in focusing media”, Phys. Rev. E, 99:2 (2019)
Rustem R. Aydagulov, Alexander A. Minakov, “Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis”, SIGMA, 14 (2018), 119, 19 pp.
Gino Biondini, “Riemann problems and dispersive shocks in self-focusing media”, Phys. Rev. E, 98:5 (2018)
El G.A., Khamis E.G., Tovbis A., “Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves”, Nonlinearity, 29:9 (2016), 2798–2836
Kotlyarov V. Minakov A., “Modulated Elliptic Wave and Asymptotic Solitons in a Shock Problem To the Modified Korteweg-de Vries Equation”, J. Phys. A-Math. Theor., 48:30 (2015), 305201
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
A. Minakov, “Asymptotics of rarefaction wave solution to the mKdV equation”, Zhurn. matem. fiz., anal., geom., 7:1 (2011), 59–86
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
V. L. Vereshchagin, “Single-Phase Averaging for the Ablowitz–Ladik Chain”, Math. Notes, 87:6 (2010), 797–806
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

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

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References:	81
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