Abstract
Depending on the physical situation, different things happen after an infinite gradient arises in the profile of a simple wave. For example, if the wave is on a liquid surface, then it simply caves in, forming foam; if it is a stream of noninteracting particles, then a multivalued situation arises in the wave profile and after the formation of “discontinuity” in the main flow, several different flows moving at very different velocities form. For sound or electromagnetic fields, however, where multivaluedness is impermissible, the way the nonlinear wave develops depends on which effect predominates in the region of the rapidly changing field, i.e., dissipative or dispersion effects. We shall now study travelling waves in nonlinear media with dissipation and dispersion.
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© 1989 Kluwer Academic Publishers
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Rabinovich, M.I., Trubetskov, D.I. (1989). Stationary Shock Waves and Solitons. In: Oscillations and Waves. Mathematics and Its Applications (Soviet Series), vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1033-1_19
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DOI: https://doi.org/10.1007/978-94-009-1033-1_19
Publisher Name: Springer, Dordrecht
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