Self focusing of acoustically excited Faraday ripples on a bubble wall

A theoretical explanation is presented to explain pattern formation during the generation of Faraday waves on a bubble wall. The theory derives the Hamiltonian formulation of the nonlinear bubble dynamics. The nonlinear Schrödinger equation for the envelope of surface modes on the bubble wall has been obtained. The solitary wave solution predicts that the shape distortions should be localized near the equator of the bubble.