1. N. Krylov and N. Bogoliubov,Introduction to Nonlinear Mechanics, translated by S. Lefshetz (Princeton University Press, Princeton, New Jersey, 1947).
2. N. Bogoliubov and Y. A. Mitropolskii,Asymptotic Methods in the Theory of Nonlinear Oscillations(Gordon and Breach Science Publishers, New York, 1961) [translated from the Russian].
3. Secular and Nonsecular Behavior for the Cold Plasma Equations
4. We are indebted to Sluijter and Montgomery who pointed out in a recently communicated Comment to this journal that the second-order frequency shift for an electromagnetic wave is a relativistic quantity. Equations (1) and (2) are based on the relativistic “cold” plasma equations and therefore differ from Eq. (50) of Ref. 3.
5. Helicon oscillations are typically excited in a metal cooled to a few degrees Kelvin in a magnetic field of 104G. Although the electrons in the metal are highly degenerate in this case, it is usually assumed that for collective oscillations with a wavelength much larger than the de Broglie wavelength of the electrons, a classical description of the electron gas has some validity. We do not enquire into the validity of this assumption here.