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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2011, Volume 7, Number 1, Pages 59–86 (Mi jmag166)  
This article is cited in 6 scientific papers (total in 6 papers)

Asymptotics of rarefaction wave solution to the mKdV equation

A. Minakov

Mathematics Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv, 61103, Ukraine
Full-text PDF (303 kB) Citations (6)
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Key words and phrases: nonlinear equations, Riemann–Hilbert problem, the steepest descent method, asymptotics.
Received: 04.04.2010
Bibliographic databases:
Document Type: Article
MSC: 35Q15,35B40
Language: English
Citation: A. Minakov, “Asymptotics of rarefaction wave solution to the mKdV equation”, Zh. Mat. Fiz. Anal. Geom., 7:1 (2011), 59–86
Citation in format AMSBIB
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\by A.~Minakov
\paper Asymptotics of rarefaction wave solution to the mKdV equation
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  • https://www.mathnet.ru/eng/jmag166
  • https://www.mathnet.ru/eng/jmag/v7/i1/p59
    • This publication is cited in the following 6 articles:
    1. Chunjiang Wang, Jian Zhang, “Inverse scattering transform for the focusing Hirota equation with asymmetric boundary conditions”, Theoret. and Math. Phys., 221:3 (2024), 2109–2131  mathnet  crossref  crossref  adsnasa
    2. 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  crossref  mathscinet  zmath  isi  scopus
    3. Bertola M. Minakov A., “Laguerre Polynomials and Transitional Asymptotics of the Modified Korteweg-de Vries Equation For Step-Like Initial Data”, Anal. Math. Phys., 9:4 (2019), 1761–1818  crossref  mathscinet  zmath  isi  scopus
    4. Iryna Egorova, Johanna Michor, Gerald Teschl, “Long-time asymptotics for the Toda shock problem: non-overlapping spectra”, Zhurn. matem. fiz., anal., geom., 14:4 (2018), 406–451  mathnet  crossref
    5. 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  mathscinet  zmath  isi  elib
    6. 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
    Citing articles in Google Scholar: Russian citations, English citations
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