TY - GEN
T1 - Time-domain evolution equation for dispersive nonlinear Rayleigh waves
AU - Ohm, Won Suk
AU - Hamilton, Mark F.
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2006
Y1 - 2006
N2 - Korteweg-de Vries (KdV) and Benjamin-Ono (BO) equations are often cited as time-domain models for nonlinear Rayleigh waves in a dispersive medium such as a coated substrate. However, these canonical equations do not account for the nonlocal nonlinearity that is a hallmark of surface acoustic waves. In this paper, a time-domain evolution equation derived for nonlinear Rayleigh waves in nondispersive isotropic media [Hamilton, Il'insky, and Zabolotskaya, J. Acoust. Soc. Am. 97, 891-897 (1995)] is extended to include dispersion due to thin-film coating. It is demonstrated that a class of soliton-like solutions resembling Mexican hats satisfies the evolution equation for the case of KdV-type dispersion, a result obtained previously by Eckl et al. [Phys. Rev. E 70, 046604 (2004)] from a frequency-domain form of the evolution equation.
AB - Korteweg-de Vries (KdV) and Benjamin-Ono (BO) equations are often cited as time-domain models for nonlinear Rayleigh waves in a dispersive medium such as a coated substrate. However, these canonical equations do not account for the nonlocal nonlinearity that is a hallmark of surface acoustic waves. In this paper, a time-domain evolution equation derived for nonlinear Rayleigh waves in nondispersive isotropic media [Hamilton, Il'insky, and Zabolotskaya, J. Acoust. Soc. Am. 97, 891-897 (1995)] is extended to include dispersion due to thin-film coating. It is demonstrated that a class of soliton-like solutions resembling Mexican hats satisfies the evolution equation for the case of KdV-type dispersion, a result obtained previously by Eckl et al. [Phys. Rev. E 70, 046604 (2004)] from a frequency-domain form of the evolution equation.
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U2 - 10.1063/1.2210335
DO - 10.1063/1.2210335
M3 - Conference contribution
AN - SCOPUS:33845990283
SN - 0735403309
SN - 9780735403307
T3 - AIP Conference Proceedings
SP - 139
EP - 142
BT - INNOVATIONS IN NONLINEAR ACOUSTICS - ISNA 17
T2 - INNOVATIONS IN NONLINEAR ACOUSTICS - ISNA17: 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum
Y2 - 18 July 2005 through 22 July 2005
ER -