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The method of multiple scales and non-linear dispersive waves

Published online by Cambridge University Press:  29 March 2006

Ali Hasan Nayfeh  and
Sayed D. Hassan
Ali Hasan Nayfeh
Affiliation:
Aerotherm Corporation, Mountain View, California Present address: Engineering Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.
Sayed D. Hassan
Affiliation:
Mathematics Department, Stanford, California
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Abstract

The method of multiple scales is used to analyze three non-linear physical systems which support dispersive waves. These systems are (i) waves on the interface between a liquid layer and a subsonic gas flowing parallel to the undisturbed interface, (ii) waves on the surface of a circular jet of liquid, and (iii) waves in a hot electron plasma. It is found that the partial differential equations that govern the temporal and spatial variations of the wave-numbers, amplitudes, and phases have the same form for all of these systems. The results show that the non-linear motion affects only the phase. For the constant wave-number case, the general solution for the amplitude and the phase can be obtained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 48 , Issue 3 , 16 August 1971 , pp. 463 - 475
Copyright
© 1971 Cambridge University Press

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