KdV Hamiltonian as a Function of Actions
Résumé
We prove that the non-linear part of the Hamiltonian of the KdV equation on the circle, written as a function of the actions, defines a continuous convex function on the l_2 space and derive for it lower and upper bounds in terms of some functions of the l_2-norm. The proof is based on a new representation of the Hamiltonian in terms of the quasimomentum, obtained via the conformal mapping theory.
Origine : Fichiers produits par l'(les) auteur(s)