Local well-posedness and wave breaking results for periodic solutions of a shallow water equation for waves of moderate amplitude

Abstract

We study the local well-posedness of a periodic nonlinear equation for surface waves of moderate amplitude in shallow water. We use an approach due to Kato which is based on semigroup theory for quasi-linear equations. We also show that singularities for the model equation can occur only in the form of wave breaking, in particular surging breakers.