The soliton is a pulse-like nonlinear wave which emerges from a collision with another soliton with its shape and speed preserved. This description, taken from the excellent review given by Scott, Chu, and McLaughlin (1973), aptly characterizes planar solitons. We shall see that solitons also exist in two and three dimensions, by extending the above characterization appropriately.
KeywordsSoliton Solution Plasma Wave Nonlinear Schrodinger Equation Breather Solution Single Soliton
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References and Suggested Reading
Key Articles, Reviews and Conference Proceedings
- Asano, N., T. Taniuti, and N. Yajima, 1969, J. Math. Phys. 10, 2020. Note that the results given in this paper for P and Q are different than equations (3.47)–(3.49) because our results are for adiabatic electrons while Asano et al. assume isothermal electrons.Google Scholar
- Jeffrey, A., and K. Kakutani, 1972, SIAM Rev. 14, 582. This is an excellent discussion of the Burgers shock wave and the KdV solitary wave.Google Scholar
- Russell, J. Scott, 1845, Report on Waves, in Report to the Fourteenth Meeting (1844) of British Assn. for Advancement of Science (London), p. 311.Google Scholar
- Scott, A. C., F. Y. F. Chu, and D. W. McLaughlin, 1973, Proc. IEEE 61, 1443. This is an excellent review article on solitons and is highly recommended to the reader.Google Scholar
- Bogoliubov, N. N., and Y. A. Mitropolsky, 1961, Asymptotic Methods in the Theory of Nonlinear Oscillations (Gordon and Breach Science Publishers, New York), Chap. I. A recent application of these methods to the laser excitation of atoms and molecules can be found in Wong et al. (1976).Google Scholar
- Jackson, J. D., 1975, Classical Electrodynamics, 2nd ed. ( J. Wiley, New York). See in particular Section 10. 8.Google Scholar