RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2019, Volume 201, Number 3, Pages 347–360 (Mi tmf9746)  

Physical parameters of solitary wave packets in shallow basins under ice cover

A. T. Il'ichev

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

Abstract: We determine the velocities and lengths of solitary envelope waves whose velocity is located in a left half-neighborhood of the phase velocity minimum in the dispersion relation for shallow basins under ice cover. The ice cover is modeled as an elastic Kirchhoff–Love ice plate. The Euler equation for the liquid layer (water) includes an additional pressure from the plate, which floats freely on the liquid surface. We consider the case of weakly nonlinear waves in the limit of long wavelengths and small amplitudes where the initial dimensionless stress in the ice cover does not exceed one third. These waves are described by a fifth-order Kawahara equation. We then compare the obtained results with the parameters found using a strongly nonlinear description. The comparison yields very good results for shallow depths of the considered basin. This phenomenon is explained by the properties of the lowest nonlinearity coefficient in the equations describing the solitary envelope waves branching from the phase velocity minimum on the dispersion curve. We discuss possible applications of the obtained results to experimental wave measurements under an ice cover.

Keywords: ice cover, solitary envelope wave, bifurcation, nonlinear Schrödinger equation, equation in quasinormal form.

Funding Agency Grant Number
Russian Science Foundation 19-71-30012
This research was supported by a grant from the Russian Science Foundation (Project No. 19-71-30012).


DOI: https://doi.org/10.4213/tmf9746

Full text: PDF file (511 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2019, 201:3, 1710–1722

Bibliographic databases:

Received: 15.05.2019
Revised: 14.08.2019

Citation: A. T. Il'ichev, “Physical parameters of solitary wave packets in shallow basins under ice cover”, TMF, 201:3 (2019), 347–360; Theoret. and Math. Phys., 201:3 (2019), 1710–1722

Citation in format AMSBIB
\Bibitem{Ili19}
\by A.~T.~Il'ichev
\paper Physical parameters of solitary wave packets in shallow basins under ice cover
\jour TMF
\yr 2019
\vol 201
\issue 3
\pages 347--360
\mathnet{http://mi.mathnet.ru/tmf9746}
\crossref{https://doi.org/10.4213/tmf9746}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4036826}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2020TMP...201.1710I}
\transl
\jour Theoret. and Math. Phys.
\yr 2019
\vol 201
\issue 3
\pages 1710--1722
\crossref{https://doi.org/10.1134/S0040577919120043}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85077603006}


Linking options:
  • http://mi.mathnet.ru/eng/tmf9746
  • https://doi.org/10.4213/tmf9746
  • http://mi.mathnet.ru/eng/tmf/v201/i3/p347

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:44
    References:5
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020