Experiments on generation of 1, 2, 4, and 6 sonoluminescent bubbles in water with an external ultrasound source in an acoustic sphere resonator with glass walls have been carried out. Theoretical examination has shown that the observed excitation frequencies could be described with a good accuracy taking into account that the velocities and pressures of the contacting media on the external and internal resonator surfaces are equal. The necessity of accounting for oscillations with non--zero self--values of angular momentum operator has been shown when describing the features of localization of several bubbles. To explain a strangely small distance between the bubbles in the case of two--bubble sonoluminescence the following possible explanations have been proposed: a) mechanism of space splitting of a mode with a singular angular momentum and b) mechanism of secondary excitation when one of the bubbles is trapped into the acoustic trap created by high--frequency vibrations arising simultaneously when the other bubble sonoluminescence occurs.
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