The generation of an undular bore in the vicinity of a wave‐breaking point is considered for the integrable Kaup–Boussinesq (KB) shallow water system. In the framework of the Whitham modulation theory, an analytic solution of the Gurevich–Pitaevskii type of problem for a generic “cubic” breaking regime is obtained using a generalized hodograph transform, and a further reduction to a linear Euler–Poisson equation. The motion of the undular bore edges is investigated in detail.
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El et al. (2005) studied this question.