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.
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
This publication is cited in the following 8 articles:
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
R. Wang, H. Ding, X. Yuan, N. Lv, L.-Q. Chen, “Different types of solitary waves in a thermo-hyperelastic neo-hookean cylindrical shell”, Compos. Struct., 243 (2020), 112178
Il'ichev A.T., Shargatov V.A., Fu Y.B., “Characterization and Dynamical Stability of Fully Nonlinear Strain Solitary Waves in a Fluid-Filled Hyperelastic Membrane Tube”, Acta Mech., 231:10 (2020), 4095–4110
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
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
Chugainova A.P., Shargatov V.A., Gorkunov S.V., Sumskoi S.I., “Regimes of Shock Wave Propagation Through Comb-Shaped Obstacles”, AIP Conference Proceedings, 2025, ed. Todorov M., Amer Inst Physics, 2018, 080002-1
V. A. Shargatov, A. P. Chugainova, S. V. Gorkunov, S. I. Sumskoi, “Analytical and numerical solutions of the shock tube problem in a channel with a pseudo-perforated wall”, JPCS, 1099 (2018), 12013–8
A T Il'ichev, “Dynamical stability of running solitary waves in fluid-filled elastic membrane tubes”, J. Phys.: Conf. Ser., 1099 (2018), 012018
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