This paper analytically investigates the weakly nonlinear propagation of a quasi-monochromatic pressure waves in an initially quiescent liquid uniformly containing many small spherical gas bubbles. A fast propagation mode induced by the incorporation of compressibility in the liquid phase is focused. The incident wave frequency is larger than the eigenfrequency of single bubble oscillations. Then, a nonlinear Schrodinger (NLS) equation describing propagation properties in a far field, can be derived in a general and systematic procedure based on the asymptotic expansion method of multiple scales (Kanagawa et al., J. Fluid Sci. Technol., 2010; Kanagawa, J. Acoust. Soc. Am., 2015) from a set of averaged equations in a two-fluid model.
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