Abstract
The interaction of long (sound) and short (ultrasound) waves propagating in a rarefied monodisperse mixture of a weakly compressible liquid with gas bubbles is considered. Using the multiscale method, the Davey-Stewartson system of equations is derived as a model of two-dimensional interaction. It is shown that, for some values of parameters, this system is reduced to an integrable form (the Davey-Stewartson I equations) and has localized solutions in the form of dromions (exponentially decaying waves of the short-wave envelope). One of the most important properties of dromions is their ability to move according to the law that governs the variations of the boundary conditions set at infinity for the long wave. It is suggested that these solutions be used for controlling the effects of ultrasound on bubbly liquids.
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