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Nonlinear wave interactions in nonlinear nonintegrable systems. (English) Zbl 1020.35082
Summary: The main goal of this article is to understand the qualitative appearances of regular arrays of pulses that come up in nonintegrable systems in a variety of contexts, particularly in fluid dynamics. It is shown that even nonintegrable systems have a kind of particle dynamics made up of solitary waves. But the interaction of these solitary waves is not absolutely “clean” as in the case of the KdV and other integrable equations.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies