Finite energy wave signals of extremal amplitude in the spatial NLS-dynamics

With the aim to find extremal properties of extreme waves, we consider waves of maximal crest (and wave) height in the model of the spatial NLS-dynamics. Using the two motion invariants momentum and Hamiltonian as constraints, we show that so-called cornered solitons provide the maximal crest heights for most pairs of feasible constraint values. At the boundary of the feasible set the well-known smooth solitons are found. We discuss the implications for the solutions of NLS evolving from an initial signal.