Abstract
Having now completed our discussion of continuous and periodic linear systems, of linear wave equations in particular, we shall now, as in Chapter 8, have a glimpse of nonlinear waves. The study of such waves is at present a large and active field of study in applied mathematics. The activity is motivated largely by the fact that the most fundamental equations of physics are nonlinear—the wave equations of general relativity and of gauge theories of particles—and by the fact that some solutions of certain nonlinear wave equations behave rather like particles even before they are subjected to quantum postulates. Partly because these particle properties appear only in the one-dimensional versions of some of these equations and partly because such versions are much simpler to analyze than more realistic versions, we shall confine our discussion to equations containing two independent variables, x and t.
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Notes
Karpman, V.I. Nonlinear Waves in Dispersive Media. New York: Pergamon, 1975.
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Eilenberger, G. Solitons. New York, Springer, 1981.
Dodd, RK., J.C. Eilbeck, J.D. Gibbon, and H.C. Morris. Solitons and Nonlinear Wave Equations. New York; Academic Press, 1982.
Drazin, P.G. Solitons. Cambridge, Cambridge Press, 1983.
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Bloch, I. (1997). Nonlinear Waves. In: The Physics of Oscillations and Waves. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0050-0_17
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DOI: https://doi.org/10.1007/978-1-4899-0050-0_17
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