Modulation of nonlinear waves in a fluid‐filled elastic tube with stenosis

Abstract

Treating the arteries as a thin-walled and prestressed elastic tube with a stenosis and the blood as a Newtonian fluid with negligible viscosity, we have studied the amplitude modulation of nonlinear waves in such a composite system by use of the reductive perturbation method. The governing evolution equation is obtained as the variable-coefficient nonlinear Schrödinger equation. It is observed that the speed of the harmonic wave increases with distance from the center of stenosis.

Integral Methods to Solve the Variable Coefficient Nonlinear Schrödinger Equation

“…where ξ 0 is an arbitrary integration constant. This solitary wave solution is similar to that solution obtained by Demiray in [1].…”

“…When we used direct integration, it was very easy to find many new exact solitary and periodic solutions. By comparison of our solutions with that obtained in [1], we have recovered those solutions and obtained many new other solutions.…”

Crank-Nicolson implicit method for the nonlinear Schrodinger equation with variable coefficient

“…The NLS equation is the simplest representative equation describing the self-modulation of one-dimensional monochromatic plane waves in dispersive media [2]. The NLS equation appears in many branches of physics and applied mathematics.…”