Modulation of nonlinear waves near the marginal state of instability in fluid-filled elastic tubes

摘要

Using the nonlinear differential equations governing the motion of a fluid-filled and prestressed long thin elastic tube, the propagation of nonlinear waves near the marginal state is examined through the use of reductive perturbation method. It is shown that the amplitude modulation near the marginal state is governed by a generalized nonlinear Schrödinger (GNLS) equation. Some exact solutions, including oscillatory and solitary waves of the GNLS equation are presented.