Nonlinear Surface Acoustic Waves and Their Associated Surface Acoustic Solitons
We obtain the nonlinear dispersion relation, and the associated displacement field, for nonlinear surface acoustic waves of shear horizontal polarization that propagate without change of form in a system that consists of a film of thickness d of a linear, cubic elastic medium bonded to a semi-infinite, nonlinear, cubic elastic medium. From the nonlinear dispersion relation we obtain the nonlinear Schrödinger equation governing the propagation of a surface acoustic soliton in this system by methods developed originally by Whitham, Yuen and Lake, and Karpman and Krushkal΄. It is found that stable solutions of this equation can exist in the system under consideration.
KeywordsSolitary Wave Rayleigh Wave Elastic Medium Surface Acoustic Wave Nonlinear Schrodinger Equation
Unable to display preview. Download preview PDF.
- 7.Strictly speaking, a soliton is a solitary wave that on colliding with another solitary wave passes through the latter without change of form and with only a small change in the phase of each. However, since the term “surface acoustic soliton” has entered the literature, and since it is less clumsy than the term “surface acoustic solitary wave,” we will use the former here.Google Scholar
- 19.V. I. Karpman and E. M. Krushkal΄: Zh. Eksp. Teor. Fiz. 55, 530 (1968) [Soviet Physics — JETP 28, 277 (1969)].Google Scholar
- 20.R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris: Solitons and Nonlinear Wave Equations (Academic Press, New York, 1982), p. 505 ff.Google Scholar
- 21.V. E. Zakharov and A. B. Shabat: Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Soviet Physics — JETP 34, 62 (1972)].Google Scholar