SUMMARYThe propagation of small-but-finite-amplitude weakly-dispersive pressure pulses in a viscoelastic fluid-filled tube is shown to be governed by a Korteweg-de Vries-Burgers (KdVB) equation. We present a direct singular perturbation theory to describe the viscoelastic modulation of solitary pressure pulses for small retardation times. The main pulse evolves so as to satisfy a leading-order energy balance resulting in an algebraic decay in the amplitude and translation speed of the solution. Higher-order energy balances imply a monotonically increasing positive phase shift.A complete description of the first-order perturbation pressure is given. A pressure shelf of finite extent is continuously excited in the lee of the propagating pulse. The shelf extends from the current location of the solitary pressure pulse to the Korteweg-Moens phase position. The transition of the pressure shelf back to a zero background state at the Korteweg-Moens phase position is accomplished through a series of viscoelastically modified spatially-decaying high-wavenumber oscillations. Ahead of the main pulse a uniformly valid perturbation pressure field is obtained via a combination WKB-power-series and similarity-solution procedure.

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