Modulational instability in magnetic fluids
Authors:
S. K. Malik and M. Singh
Journal:
Quart. Appl. Math. 43 (1985), 57-64
MSC:
Primary 76W05; Secondary 76E25
DOI:
https://doi.org/10.1090/qam/782256
MathSciNet review:
782256
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Abstract: A weakly nonlinear evolution of two dimensional wave packets on the surface of a magnetic fluid in the presence of a tangential magnetic field is presented taking into account the surface tension. It is shown that the magnetic field has a stabilizing influence on the modulational instability.
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M. J. Lighthill, Contribution to the theory of waves in nonlinear dispersive systems, J. Inst. Maths. Applics. 1, 269–306 (1965)
T. B. Benjamin and J. E. Feir, The disintegration of wave trains on deep water. Part I. Theory, J. Fluid Mech. 27, 417–430 (1967)
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- Ali Hasan Nayfeh, Perturbation methods, John Wiley & Sons, New York-London-Sydney, 1973. Pure and Applied Mathematics. MR 0404788
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R. E. Zelazo and J. R. Melcher, Dynamics and stability of ferrofluids: Surface interactions, J. Fluid Mech. 39, 1–24 (1969)
M. D. Cowley and R. E. Rosensweig, The interfacial instability of a ferro-magentic fluid, J. Fluid Mech. 30, 671–688 (1967)
M. J. Lighthill, Contribution to the theory of waves in nonlinear dispersive systems, J. Inst. Maths. Applics. 1, 269–306 (1965)
T. B. Benjamin and J. E. Feir, The disintegration of wave trains on deep water. Part I. Theory, J. Fluid Mech. 27, 417–430 (1967)
G. B. Whitham, Linear and nonlinear waves, Wiley, New York, 1974
H. Hasimoto and H. Ono, Nonlinear modulation of gravity waves, J. Phys. Soc. Jap. 33, 805–829 (1972)
A. Davey and K. Stewartson, On three-dimensional packets of surface waves, Proc. Roy. Soc. Lond., Series A, 338, 101–110 (1974)
S. K. Malik and M. Singh, Nonlinear dispersive instabilities in magnetic fluids, (Simon Fraser University reprint)
A. H. Nayfeh, Perturbation methods, Wiley, New York, 1973
V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focussing and one-dimensional self-modulating waves in nonlinear media, Sov. Phys. JETP 34, 62–69 (1972)
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Article copyright:
© Copyright 1985
American Mathematical Society
