Abstract
The weakly nonlinear standing waves on the surface of a self-gravitating incompressible fluid column are investigated in the presence of, a uniform axial-magnetic field. By use of the method of multiple scales, we have shown that near the critical wave number, the amplitude modulation of a standing wave can be described by a nonlinear Schrödinger equation with the roles of time and space variable interchanged. It is demonstrated that in presence of a magnetic field, the system is always stable near the critical wave number.
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References
Chandrasekhar, S. and Fermi, E.: 1953,Astrophys. J. 118, 116.
Chhabra, R. K. and Trehan, S. K.: 1989,Astrophys. Space. Sci. 158, 67.
Kakutani, T., Inoue, Y., and Kan, T.: 1974,J. Phys. Soc. Japan 37, 529.
Malik, S. K. and Singh, M.: 1979,Astrophys. Space Sci. 66, 133.
Lardner, R. W. and Trehan, S. K.: 1983,Astrophys. Space Sci. 96, 261.
Nayfeh, A. H.: 1970,Phys. Fluids 13, 841.
Nayfeh, A. H. and Hassan, S. D.: 1971,J. Fluid Mech. 48, 463.
Tassoul, J. L. and Aubin, G.: 1974.,J. Math. Anal. Appl. 45, 116.
Trehan, S. K. and Lardner, R. W.: 1990,Int. J. Eng. Sci. (in press).
Wang, D. P.: 1968,J. Fluid Mech. 34, 299.
Yuen, M. C.: 1968,J. Fluid Mech 33, 151.
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Department of Chemical Engineering, and Technology
Department of Mathematics
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Chhabra, R.K., Trehan, S.K. Nonlinear standing waves on the surface of a self-gravitating cylinder. Astrophys Space Sci 163, 341–349 (1990). https://doi.org/10.1007/BF00655751
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DOI: https://doi.org/10.1007/BF00655751