Finite-amplitude surface waves in electrohydrodynamics
Authors:
Rama Kant, R. K. Jindia and S. K. Malik
Journal:
Quart. Appl. Math. 39 (1981), 23-32
DOI:
https://doi.org/10.1090/qam/99627
MathSciNet review:
QAM99627
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Abstract: The stability of weakly nonlinear waves on the surface of a fluid layer in the presence of an applied electric field is investigated by using the derivative expansion method. A nonlinear Schrödinger equation for the complex amplitude of quasi-monochromatic traveling wave is derived. The wave train of constant amplitude is unstable against modulation. The equation governing the amplitude modulation of the standing wave is also obtained which yields the nonlinear cut-off wave number.
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M. Hasimoto and H. Ono, Nonlinear modulation of gravity waves, J. Phys. Soc. Japan 33, 805 (1972)
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Lord Rayleigh, The theory of sound, Macmillan, 1894
G. G. Stokes, On the theory of oscillatory waves, in Mathematical and physical papers, Cambridge University Press, 1880, Vol. 1, p. 197
D. H. Michael, Nonlinear effects on electrohydrodynamic surface wave propagation, Quart. App. Math. 35, 345 (1977)
B. K. Shivamoggi, Nonlinear stability of surface waves in electrohydrodynamics, Quart. App. Math. 37, 424 (1979)
M. J. Lighthill, Waves in fluids, Cambridge University Press, 1978
G. B. Whitham, Linear and nonlinear waves, John Wiley, New York, 1974
V. I. Karpman, Nonlinear waves in dispersive media, Pergamon Press, 1975
A. H. Nayfeh, Perturbation methods, John Wiley, New York, 1973
M. Hasimoto and H. Ono, Nonlinear modulation of gravity waves, J. Phys. Soc. Japan 33, 805 (1972)
T. Kakutani, Y. Inoue and T. Kan, Nonlinear capillary waves on the surface of liquid column, J. Phys. Soc. Japan 37, 529 (1974)
V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Soviet Physics J.E.T.P. 34, 62 (1972)
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Article copyright:
© Copyright 1981
American Mathematical Society
