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

Abstract

Summary: One-dimensional wave propagation near the marginal state of modulational instability in an infinitely long, straight and homogeneous nonlinear elastic tube filled with an incompressible inviscid fluid is considered. Using the reductive perturbation method, the amplitude modulation of weakly nonlinear waves is examined. It is shown that the amplitude modulation of these waves near the marginal state is governed by a generalized nonlinear Schrödinger equation (GNLS). Some exact solutions including oscillatory and solitary waves of the GNLS equation are presented.