A note on the application of Whitham's method to nonlinear waves in dispersive media
- 1 February 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Plasma Physics
- Vol. 11 (1), 63-76
- https://doi.org/10.1017/s0022377800024478
Abstract
In this paper, a method developed by Whitham for obtaining equations governing the slow variation of finite-amplitude wave trains, is slightly modified. The relevant equations describing wave-wave interaction, and self-action are derived. The stability of a finite-amplitude wave train is treated in two different ways. The possibility of having a ‘solitary modulation’ on a finite-amplitude wave train is pointed out.Keywords
This publication has 21 references indexed in Scilit:
- An approach to linear and non-linear wave coupling using dispersion and energy relations †International Journal of Electronics, 1972
- Non-linear interaction of positive and negative energy waves †International Journal of Electronics, 1970
- Self-trapping and self-focusing of electromagnetic waves in a plasmaPhysics Letters A, 1968
- Instability of periodic wavetrains in nonlinear dispersive systemsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1967
- The disintegration of wave trains on deep water Part 1. TheoryJournal of Fluid Mechanics, 1967
- Convective and absolute instabilityNuclear Fusion, 1966
- Feynman diagrams and interaction rules of wave‐wave scattering processesReviews of Geophysics, 1966
- Self-Trapping of Optical BeamsPhysical Review Letters, 1964
- Some General Properties of Nonlinear Elements-Part I. General Energy RelationsProceedings of the IRE, 1956
- XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wavesJournal of Computers in Education, 1895