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Wave breaking for nonlinear nonlocal shallow water equations. (English) Zbl 0923.76025
The authors continue their analysis published in [Math. Ann. 312, No. 3, 403-416 (1998), see the preceding review; Zbl 0923.76012]. Namely, they study the occurrence of a singularity and its nature in the wave motion by using the nonlinear nonlocal shallow water theory (blow-up phenomenon). The aim is to avoid some additional assumptions made by previous authors who studied the problem. The construction is based on theorem 2.1 which is applied to different forms of shallow water equations.

MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q53 KdV equations (Korteweg-de Vries equations)
35Q35 PDEs in connection with fluid mechanics
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