Solitary waves in fluid-filled elastic tubes: weakly dispersive case
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In the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and the approximate equations of an incompressible inviscid fluid, the propagation of weakly nonlinear waves, in such a medium is studied through the use of the modified multiple expansion method. It is shown that the evolution of the lowest order (first-order) term in the perturbation expansion may be described by the Korteweg-de Vries (KdV) equation. The governing equation for the second-order terms and the localized travelling wave solution for these equations are also obtained. The applicability of the present model to flow problems in arteries is discussed.