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Solitary waves in fluid-filled elastic tubes: existence, persistence, and the role of axial displacement

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Abstract

We reexamine the problem of solitary wave propagation in a fluid-filled elastic membrane tube using a much simplified procedure. It is shown that there may exist four families of solitary waves with speeds close to those given by the linear dispersion relation, whether the fluid is initially stationary or not, and that it is not asymptotically consistent to neglect the axial displacement even in a long-wave approximation. It is also shown that the solitary wave solutions obtained by neglecting higher-order terms persist for the full system of equations in the sense that the full system has solutions of the solitary wave type and each exact solution is uniformly approximated by the corresponding leading-order solution.

Acceptance Date Jan 20, 2010
Publication Date Feb 24, 2010
Publicly Available Date Mar 29, 2024
Journal IMA Journal of Applied Mathematics
Print ISSN 0272-4960
Publisher Oxford University Press
Pages 257 - 268
DOI https://doi.org/10.1093/imamat/hxq004
Keywords Solitary waves, membrane tubes, bifurcation, nonlinear elasticity
Publisher URL https://doi.org/10.1093/imamat/hxq004

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