Extremal periodic wave profiles

Abstract. As a contribution to deterministic investigations into extreme fluid surface waves, in this paper wave profiles of prescribed period that have maximal crest height will be investigated. As constraints the values of the momentum and energy integrals are used in a simplified description with the KdV model. The result is that at the boundary of the feasible region in the momentum-energy plane, the only possible profiles are the well known cnoidal wave profiles. Inside the feasible region the extremal profiles of maximal crest height are "cornered" cnoidal profiles: cnoidal profiles of larger period, cut-off and periodically continued with the prescribed period so that at the maximal crest height a corner results.