Nonlinear oscillations of a bubble under various boundary conditions

The method of many scales is used to examine the nonlinear oscillations of a spherical gas bubble that occur under the action of a periodically changing external pressure in a spherical volume of inviscid, incompressible liquid and in a liquid flow. The influence of the finite dimensions of the volume and liquid flow velocity on the conditions for the existence of certain types of the equilibrium state of an oscillating bubble is analyzed.