Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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 | References | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] Lord Rayleigh, Annual General Meeting, Proc. Lond. Math. Soc. 10 (1878/79), 1–3. MR 1576178, https://doi.org/10.1112/plms/s1-10.1.1
  • [2] G. G. Stokes, On the theory of oscillatory waves, in Mathematical and physical papers, Cambridge University Press, 1880, Vol. 1, p. 197
  • [3] D. H. Michael, Nonlinear effects on electrohydrodynamic surface wave propagation, Quart. App. Math. 35, 345 (1977)
  • [4] B. K. Shivamoggi, Nonlinear stability of surface waves in electrohydrodynamics, Quart. App. Math. 37, 424 (1979)
  • [5] James Lighthill, Waves in fluids, Cambridge University Press, Cambridge-New York, 1978. MR 642980
  • [6] G. B. Whitham, Linear and nonlinear waves, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Pure and Applied Mathematics. MR 0483954
  • [7] V. I. Karpman, Non-linear waves in dispersive media, Revised edition, Pergamon Press, Oxford-New York-Toronto, Ont., 1975. Translated from the Russian by F. F. Cap; International Series of Monographs in Natural Philosophy, Vol. 71. MR 0455792
  • [8] Ali Hasan Nayfeh, Perturbation methods, John Wiley & Sons, New York-London-Sydney, 1973. Pure and Applied Mathematics. MR 0404788
  • [9] M. Hasimoto and H. Ono, Nonlinear modulation of gravity waves, J. Phys. Soc. Japan 33, 805 (1972)
  • [10] T. Kakutani, Y. Inoue and T. Kan, Nonlinear capillary waves on the surface of liquid column, J. Phys. Soc. Japan 37, 529 (1974)
  • [11] V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Ž. Èksper. Teoret. Fiz. 61 (1971), no. 1, 118–134 (Russian, with English summary); English transl., Soviet Physics JETP 34 (1972), no. 1, 62–69. MR 0406174

Additional Information

DOI: https://doi.org/10.1090/qam/99627
Article copyright: © Copyright 1981 American Mathematical Society

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