Maksimov, Alexey O.; Leighton, Timothy G.; Birkin, Peter R. Self focusing of acoustically excited Faraday ripples on a bubble wall. (English) Zbl 1220.35012 Phys. Lett., A 372, No. 18, 3210-3216 (2008). 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. Cited in 3 Documents 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 Keywords:bubble; Faraday ripples; Hamiltonian dynamics; solitary wave PDFBibTeX XMLCite \textit{A. O. Maksimov} et al., Phys. Lett., A 372, No. 18, 3210--3216 (2008; Zbl 1220.35012) Full Text: DOI References: [1] Birkin, P. R.; Watson, Y. E.; Leighton, T. G.; Smith, K. L., Langmuir Surfaces Colloids, 18, 2135 (2002) [2] Watson, Y. E.; Birkin, P. R.; Leighton, T. G., Ultrasonics Sonochem., 10, 65 (2003) [3] Leighton, T. G., Int. J. Mod. Phys. B, 18, 3267 (2004) [4] Wu, J.; Keolian, R.; Rudnick, I., Phys. Rev. Lett., 52, 1421 (1984) [5] Miles, J., J. Fluid Mech., 148, 451 (1984) [6] Larraza, A.; Putterman, S., J. Fluid Mech., 148, 443 (1984) [7] Zakharov, V. E., J. Appl. Mech. Tech. Phys., 2, 190 (1968) [8] Benjamin, T. B.; Olver, P. J., J. Fluid Mech., 125, 137 (1982) [9] Benjamin, T. B., J. Fluid Mech., 181, 349 (1987) [10] Maksimov, A. O., (Atchley, A.; Sparrow, V.; Keolian, R. M., Innovations in Nonlinear Acoustics (2006), AIP: AIP New York), 516-519 [11] Maksimov, A. O., J. Exp. Theor. Phys.. J. Exp. Theor. Phys., Zh. Eksp. Teor. Fiz., 133, 2, 412 (2008), (in Russian) [12] Faraday, M., Philos. Trans. R. Soc. London, 121, 319 (1831) [13] Video: http://www.isvr.soton.ac.uk/fdag/Faraday.htm; Video: http://www.isvr.soton.ac.uk/fdag/Faraday.htm [14] Maksimov, A. O.; Leighton, T. G., ACUSTICA-Acta Acustica, 87, 322 (2001) [15] Maksimov, A. O., J. Sound Vibration, 283, 915 (2005) [16] Maksimov, A. O.; Leighton, T. G.; Birkin, P. R., (Atchley, A.; Sparrow, V.; Keolian, R. M., Innovations in Nonlinear Acoustics (2006), AIP: AIP New York), 512-515 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.