Work: Nonlinear resonance and their manifestation in acoustics of bubble media. Pacific Ocean Institute.

Main results: Acoustics technique for characterising bubble populations within liquids is regarded. Acoustical scattering from bubble at resonance is several orders greater than off resonance. The difference between the compressibility of gas in the bubble and surrounding liquid leads to the easy manifestation of nonlinear effects, the simplest of which is the presence of harmonics at 2, 3, etc. of the pure tone driving frequency in the scattering signal. However, these nonlinear effects associated with the bubble pulsation of finite amplitude are not reduced to the generation of harmonics only. The nonlinear resonance characterised by multystable oscillations states arising from the saddle-node bifurcation is the most brilliance example. There are a number of effects where the bifurcation of bubble oscillations becomes apparent. To propose a new technique for bubble sizing by use the ability of a bubble as a nonlinear oscillatory system to amplify weak signal near the threshold of dynamical stability was the emphasis of the study. The analytical as well as numerical solutions have been derived for the nonlinear bubble response to the modulation driving pressure. The magnitude and the form of the acoustic pressure reradiated by the nonlinear oscillating bubble near the threshold of dynamical stability are drastically different from the modulation of incident wave and enable to characterise the bubble population in liquid.