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Self focusing of acoustically excited Faraday ripples on a bubble wall. (English) Zbl 1220.35012

Summary: 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.

MSC:

35B36 Pattern formations in context of PDEs
74K25 Shells
74J35 Solitary waves in solid mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
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References:

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