KdV Hamiltonian as function of actions

Evgeny Korotyaev; Sergei Kuksin

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arXiv · 1110.4475

KdV Hamiltonian as function of actions

Evgeny Korotyaev·Sergei Kuksin

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Abstract

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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Evgeny Korotyaev, Sergei Kuksin. 2011-10-20. KdV Hamiltonian as function of actions. https://arxiv.org/abs/1110.4475

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