This study theoretically investigates plane progressive quasi-monochromatic waves in an initially quiescent compressible liquid containing many spherical gas bubbles, on the basis of the derivation of a nonlinear wave equation that represents waves propagating at a high phase velocity induced by taking the effect of liquid compressibility in consideration. The governing equations for bubbly flows are composed of the conservation equations of mass and momentum, the equation of bubble dynamics as radial oscillations, and so on. By using the method of multiple scales with an appropriate choice of set of scaling relations of nondimensional parameters, the nonlinear Schrödinger (NLS) equation with an attenuation term and some correction terms can be derived from the governing equations. The decrease in the group velocity in a far field is then clarified. The dependence of waveform on wavenumber is implied.

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