Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Nonlinear surface waves in self-gravitating fluids

Authors: S. K. Malik and M. Singh
Journal: Quart. Appl. Math. 38 (1980), 235-240
MSC: Primary 76B15; Secondary 35B40, 76E20
DOI: https://doi.org/10.1090/qam/580881
MathSciNet review: 580881
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Abstract: The weakly nonlinear disturbances in a self-gravitating, incompressible, inviscid fluid slab are studied. When the wave number is equal to the critical wave number, the amplitude modulation results in nonlinear Schrodinger equation. The finite-amplitude standing wave is stable against modulation. The nonlinear cutoff wave number is also obtained.

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

  • [1] R. S. Oganesjan, Gravitational instability of a layer relative to two- dimensional transverse disturbances, Soviet Astronom. AJ 4 (1960), 434–439. MR 0128988
  • [2] B. B. Chakraborty, Stability of a gravitating fluid layer of uniform thickness in the presence of Coriolis force and a magnetic field, Indian J. Phys. 38 (1964), 490–498. MR 0189725
  • [3] J. L. Tassoul and H. Dedic, Finite amplitude disturbances in self-gravitating media, Astron. Astrophys. 26, 79 (1973)
  • [4] G. B. Whitham, Linear and non-linear waves, Wiley, New York, 1973
  • [5] H. Hasimoto and H. Ono, Non-linear modulation of gravity waves, J. Phys. Soc. Japan 33, 805 (1972)
  • [6] T. Kakutani and N. Sugimoto, Krylov-Bogoliubov-Mitropolsky method for nonlinear wave modulation, Phys. Fluids 17 (1974), 1617–1625. MR 0351257, https://doi.org/10.1063/1.1694942

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DOI: https://doi.org/10.1090/qam/580881
Article copyright: © Copyright 1980 American Mathematical Society

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