The method of multiple scales and non-linear dispersive waves
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.(Published Online March 29 2006)
(Received October 1 1970)
(Revised February 8 1971)
p1 Present address: Engineering Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.