MODULATION OF WAVES NEAR THE MARGINAL STATE OF INSTABILITY IN FLUID-FILLED DISTENSIBLE TUBES

One-dimensional wave propagation near the marginal state of modulation al instability in an infinitely long, straight and homogeneous nonline ar elastic tube filled with an incompressible, inviscid fluid is consi dered. Using the reductive perturbation method, the amplitude modulati on of weakly nonlinear waves is examined. It is shown that the amplitu de modulation of these waves near the marginal state is governed by a generalized nonlinear Schrodinger equation (GNLS). Some exact solution s including oscillatory and solitary waves of the GNLS equation are pr esented.