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Solitons in Water-air Mixtures: Solution of the Acoustic - bubble Vibration Coupling System

In this paper we study the existence of solitary waves in a bubbly liquid by resolving numerically a system of differential equations written in acoustic pressure and bubble volume variation. The model couples the pressure field to the bubble dynamics, by taking into account viscous and inertial terms, and without any restriction on the wave frequency content. This leads to the presence of nonlinearity, dissipation, and dispersion of the acoustic pressure field. We show here that for a positive and highamplitude excitation signal, the balance between nonlinearity and dispersion leads to the existence and propagation of a solitary wave. We also demonstrate that this solitary wave verifies the main properties which allow us to call it soliton. The system of differential equations we use is wider than the Korteweg-de Vries equation, it is more realistic: bubble dynamics, attenuation due to bubbles. ... Conclusions about coincidences and differences between both models are given. We show that some soliton solutions of the set of equations we use do not verify the restrictions of the Korteweg-de Vries equation (CO ω0, where CO is the pressure wave frequency and ω0 is the bubble resonance frequency), i.e., that apart from the KdV solitonlike solution, there are many solitary waves which verify the properties of solitons. Only for low amplitudes the KdV soliton solution coincides with our results. In all the other cases the KdV solution is not valid. Acoustic pressure and bubble volume variation solitons are obtained.