In this paper, a sequel to two others [1, 2], some extensions and improvements of this earlier work are presented. Among these
are: A more precise version of the proof of the basic canonical theorem, some considerations on conservation laws and their
relation, a more complete treatment of the stability of the models, especially with respect to the wave amplitude, a short
treatment of the
... [Show full abstract] Lagrangian version of the theory, a stable discrete model which might be useful for numerical experiments
and an extension of the method to the case of slowly varying water depth.