Amplitude modulation of nonlinear waves in a thick elastic tube filled with an inviscid fluid

Abstract

In the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thick tube and the approximate equations of an incompressible inviscid fluid, and then utilizing the reductive perturbation technique the amplitude modulation of weakly nonlinear waves is examined. It is shown that the amplitude modulation of these waves is governed by a nonlinear Schrödinger(NLS) equation. The range of modulational instability of the monochromatic wave solution with the initial deformation, material and geometrical characteristics is discussed for some elastic materials.Mathematics Subject Classification (1991). 76B25, 73D35, 73G05.