This article is cited in 6 scientific papers (total in 6 papers)
Stability of solitary waves in membrane tubes: A weakly nonlinear
A. T. Il'ichev
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
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.
membrane tube, solitary wave, bifurcation, orbital stability.
|Russian Science Foundation
|This research was supported by a grant from the Russian Science Foundation (Project No. 14-50-00005).
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Theoretical and Mathematical Physics, 2017, 193:2, 1593–1601
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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\paper Stability of solitary waves in membrane tubes: A~weakly nonlinear
\jour Theoret. and Math. Phys.
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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
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A. T. Il'ichev, “Dynamics and spectral stability of soliton-like structures in fluid-filled membrane tubes”, Russian Math. Surveys, 75:5 (2020), 843–882
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