Lie group analysis is applied to the nonlinear bubble dynamics accounting both distortion and breathing modes according to the perfect-liquid model. The Hamiltonian formulation of the problem has been presented and the closed form of the Hamiltonian as a functional of canonical variables has been obtained. The equations of the prolongation theory have been derived and particular solutions corresponding subgroups of the full symmetry group have been determined. The availability of certain continuous group of symmetry generally offers a possibility of reducing the order of the corresponding differential equation. It appears possible to describe analytically the nonlinear dynamics of a bubble driven by an external perturbation in the conditions ensuring the scale invariance. The efficiency of bubble extension under the action of a periodically prolonged scale-invariant external acoustic field has been studied.
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