Analysis of modulational instability of waves in the fluid-filled elastic tube

In this paper, we investigate the modulational instability of waves within a fluid-filled elastic tube considering the fluid viscosity. Through the reductive perturbation method, we derived a modified Nonlinear Schrödinger Equation (NLSE) with damping term for the system. Based on the modified NLSE, we found that modulational instability exists in this system though the fluid viscosity is considered. Both the instability and the stability region are given. Furthermore, the growth rate of the instability is obtained. The dependence of the growth rate on the system parameters such as perturbation wave length, the background wave length, the viscosity of the fluid and the elasticity of the tube is given in the present paper. It indicates that the fluid viscosity refrain the modulational instability. The results may be used to predict the production of the rogue wave in this system, as well as to the other similar system.