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TMF, 1995, Volume 104, Number 3, Pages 393–419 (Mi tmf1346)  

This article is cited in 8 scientific papers (total in 8 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

Abstract: The focusing nonlinear Schrödinger equation with finite-density boundary conditions as $|x|\to \infty$ is considered. The asymptotic behavior of the solution as $t\to \infty$ is investigated by means of the complex theory of $\zeta$ deformations of Whitham.

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English version:
Theoretical and Mathematical Physics, 1995, 104:3, 1078–1097

Bibliographic databases:

Received: 27.10.1994

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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\by R.~F.~Bikbaev
\paper Complex Whitham deformations in the problems with ``integrable instability''
\jour TMF
\yr 1995
\vol 104
\issue 3
\pages 393--419
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1607001}
\zmath{https://zbmath.org/?q=an:0853.35111}
\transl
\jour Theoret. and Math. Phys.
\yr 1995
\vol 104
\issue 3
\pages 1078--1097
\crossref{https://doi.org/10.1007/BF02068740}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995UE86800002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. L. Vereshchagin, “Single-Phase Averaging for the Ablowitz–Ladik Chain”, Math. Notes, 87:6 (2010), 797–806  mathnet  crossref  crossref  mathscinet  isi  elib
    2. 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
    3. 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
    4. 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
    5. 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
    6. 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  crossref  isi
    7. 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  crossref  mathscinet  zmath  isi  elib  scopus
    8. 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.  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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