KdV Hamiltonian as function of actions

Details KdV Hamiltonian as function of actions KdV Hamiltonian as function of actions

2011-10-20

arxiv.org/abs/1110.4475v1

Mathematics

Dynamical Systems

21 pages, 5 figurs

Scientific paper

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 $\ell^2$ space and derive for it lower and upper bounds in terms of some functions of the $\ell^2$-norm. The proof is based on a new representation of the Hamiltonian in terms of the quasimomentum and its analysis using the conformal mapping theory.

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