The Study On Nonlinear Wave And Modulation Instability In A Fluid-filled Elastic Tube

With the continuous development of modern science and technology,people pay more attention to the nonlinear effects in many branches of science.The study of nonlinear effect of the system can help people to understand complicated phenomena.The typical nonlinear phenomena include chaos,fractals,turbulence and nonlinear waves.We know that the nonlinear Schr(?)dinger equation is an important model to explore the nonlinear effects of systems.The solutions of nonlinear Schr(?)dinger equation,such as soliton solution,breather solutions and rouge wave solutions all can reflect real physical phenomena.The model of the fluid-filled elastic tube can be used to describe the blood artery.The effect of the fluid-filled elastic tube system parameters on these nonlinear waves and the modulational instability is stuied.This study can help us to understand the nonlinear wave phenomena in fluid-filled elastic tube as well as the other nonlinear system.The details are as follows:1.Introducing a nonlinear system: a fluid-filled elastic tube.The nonlinear Schr(?)dinger equation in fluid-filled elastic tube is obtained by using reduction perturbation method.Some solutions of the nonlinear Schr(?)dinger equation are used to describe the Kuznetsov-Ma breathers,Akhmedievc breathers,rogue wave solitons,and bright solitons.It is found that the kinds of these nonlinear waves are determined by the parameter a and b(a is the amplitude of the background wave.b determines the shape of the initial nonlinear local wave).The effects of the parameter ba / on the frequency and amplitude of the nonlinear wave are studied.The effect of the fluid-filled elastic tube system parameters on nonlinear waves amplitude and wave velocity is also discussed.2.The fluid-filled elastic tube is still studied in this work,but on which the viscosity of the fluid is considered.By considering the fluid viscosity,the nonlinear Schr(?)dinger equation of fluid-filled elastic tube is obtained.It seems that the rogue wave may be produced by the modulation instability.Therefore,based on the nonlinear Schr(?)dinger equation and the linear stability analysis method,the growth rate of modulation instability of the waves in the fluid-filled elastic tube is obtained.The effect of elastic tube system parameters on the growth rate of modulation instability is also studied.