  In this paper, we consider the explicit wave-breaking mechanism and its
dynamical behavior near this singularity for the generalized b-equation. This
generalized b-equation arises from the shallow water theory, which includes the
Camassa-Holm equation, the Degasperis-Procesi equation, the Fornberg-Whitham
equation, the Korteweg-de Vires equation and the classical b-equation. More
precisely, we find that there exists an explicit self-similar blowup solution
for the generalized b-equation. Meanwhile, this self-similar blowup solution is
asymptotic stability in a parameters domain, but instability in other
parameters domain.
