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TMF, 2017, Volume 193, Number 2, Pages 214–224 (Mi tmf9317)  

This article is cited in 2 scientific papers (total in 2 papers)

Stability of solitary waves in membrane tubes: A weakly nonlinear analysis

A. T. Il'ichev

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

Abstract: We study the problem of the stability of solitary waves propagating in fluid-filled membrane tubes. We consider only waves whose speeds are close to speeds satisfying a linear dispersion relation (it is well known that there can be four families of solitary waves with such speeds), i.e., the waves with small (but finite) amplitudes branching from the rest state of the system. In other words, we use a weakly nonlinear description of solitary waves and show that if the solitary wave speed is bounded from zero, then the solitary wave itself is orbitally stable independently of whether the fluid is in the rest state at the initial time.

Keywords: membrane tube, solitary wave, bifurcation, orbital stability.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This research was supported by a grant from the Russian Science Foundation (Project No. 14-50-00005).


DOI: https://doi.org/10.4213/tmf9317

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English version:
Theoretical and Mathematical Physics, 2017, 193:2, 1593–1601

Bibliographic databases:

Document Type: Article
Received: 12.12.2016
Revised: 22.03.2017

Citation: A. T. Il'ichev, “Stability of solitary waves in membrane tubes: A weakly nonlinear analysis”, TMF, 193:2 (2017), 214–224; Theoret. and Math. Phys., 193:2 (2017), 1593–1601

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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, S. I. Sumskoi, V. A. Shargatov, “Unsteady flows in deformable pipes: the energy conservation law”, Proc. Steklov Inst. Math., 300 (2018), 68–77  mathnet  crossref  crossref  isi  elib
    2. V. A. Shargatov, A. P. Chugainova, S. V. Gorkunov, S. I. Sumskoi, “Flow structure behind a shock wave in a channel with periodically arranged obstacles”, Proc. Steklov Inst. Math., 300 (2018), 206–218  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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