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Tr. Mat. Inst. Steklova, 2015, Volume 289, Pages 163–177 (Mi tm3614)  

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

Envelope solitary waves and dark solitons at a water–ice interface

A. T. Il'ichev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: The article is devoted to the study of some self-focusing and defocusing features of monochromatic waves in basins with horizontal bottom under an ice cover. The form and propagation of waves in such basins are described by the full 2D Euler equations. The ice cover is modeled by an elastic Kirchhoff–Love plate and is assumed to be of considerable thickness so that the inertia of the plate is taken into account in the formulation of the model. The Euler equations involve the additional pressure from the plate that is freely floating at the surface of the fluid. Obviously, the self-focusing is closely connected with the existence of so-called envelope solitary waves, for which the envelope speed (group speed) is equal to the speed of filling (phase speed). In the case of defocusing, solitary envelope waves are replaced by so-called dark solitons. The indicated families of solitary waves are parametrized by the wave propagation speed and bifurcate from the quiescent state. The dependence of the existence of envelope solitary waves and dark solitons on the basin's depth is investigated.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968515020090

Full text: PDF file (286 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 289, 152–166

Bibliographic databases:

UDC: 532.59
Received: February 15, 2015

Citation: A. T. Il'ichev, “Envelope solitary waves and dark solitons at a water–ice interface”, Selected issues of mathematics and mechanics, Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov, Tr. Mat. Inst. Steklova, 289, MAIK Nauka/Interperiodica, Moscow, 2015, 163–177; Proc. Steklov Inst. Math., 289 (2015), 152–166

Citation in format AMSBIB
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\paper Envelope solitary waves and dark solitons at a water--ice interface
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov
\serial Tr. Mat. Inst. Steklova
\yr 2015
\vol 289
\pages 163--177
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968515020090}
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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. A. T. Il'ichev, Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, 2016, no. 3, 37–47  mathnet  crossref
    2. V. V. Markov, G. B. Sizykh, “Exact solutions of the Euler equations for some two-dimensional incompressible flows”, Proc. Steklov Inst. Math., 294 (2016), 283–290  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. A. T. Il'ichev, A. P. Chugainova, “Spectral stability theory of heteroclinic solutions to the Korteweg–de Vries–Burgers equation with an arbitrary potential”, Proc. Steklov Inst. Math., 295 (2016), 148–157  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. Il'ichev A.T., “Solitary wave packets beneath a compressed ice cover”, Fluid Dyn., 51:3 (2016), 327–337  crossref  mathscinet  zmath  isi  scopus
    5. A. T. Il'ichev, “Stability of solitary waves in membrane tubes: A weakly nonlinear analysis”, Theoret. and Math. Phys., 193:2 (2017), 1593–1601  mathnet  crossref  crossref  adsnasa  isi  elib
    6. A. Il'ichev, “Physical parameters of envelope solitary waves at a water-ice interface”, Mathematical Methods and Computational Techniques in Science and Engineering II, AIP Conf. Proc., 1982, ed. N. Bardis, Amer. Inst. Phys., 2018, 020036-1  crossref  isi  scopus
    7. A. T. Il'ichev, “Envelope solitary waves at a water-ice interface: the case of positive initial tension”, Math. Montisnigri, 43 (2018), 49–57  mathscinet  isi
    8. Il'ichev A.T., Tomashpolskii V.J., “Characteristic Parameters of Nonlinear Surface Envelope Waves Beneath An Ice Cover Under Pre-Stress”, Wave Motion, 86 (2019), 11–20  crossref  mathscinet  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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