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Nonlinear wave interactions for the Benjamin-Ono equation. (English) Zbl 1156.35460
Summary: We study the interaction of suitable small and high frequency waves evolving by the flow of the Benjamin-Ono equation. As a consequence, we prove that the flow map of the Benjamin-Ono equation cannot be uniformly continuous on bounded sets of \(H^s(\mathbb R)\) for \(s>0\).

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35K15 Initial value problems for second-order parabolic equations
35K55 Nonlinear parabolic equations
76B55 Internal waves for incompressible inviscid fluids
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