Solitary waves in fluid-filled elastic tubes: existence, persistence, and the role of axial displacement. (English) Zbl 1189.35386

Fu, Y. B.; Il’ichev, A. T.

IMA J. Appl. Math. 75, No. 2, 257-268 (2010).

Summary: 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.

MSC:

35R35	Free boundary problems for PDEs
35Q92	PDEs in connection with biology, chemistry and other natural sciences
76Z05	Physiological flows
92C35	Physiological flow
74F10	Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
35C08	Soliton solutions

Keywords:

solitary waves; membrane tubes; bifurcation; nonlinear elasticity