Contributions of higher order terms to nonlinear waves in fluid-filled elastic tubes: strongly dispersive case

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, and then utilizing the modified reductive perturbation technique presented by us [15] the amplitude modulation of weakly nonlinear waves is examined. It is shown that the first order term in the perturbation expansion is governed by a nonlinear Schrödinger equation and the second order term is governed by the linearized Schrödinger equation with a nonhomogeneous term. In the longwave limit a travelling wave type of solution to these equations are also given.