On the convexity of the KdV Hamiltonian

Abstract

We prove that the nonlinear part $H^{\ast }$ of the KdV Hamiltonian $H^{kdv}$, when expressed in action variables $I=(I_n{)}_{n\ge 1}$, extends to a real analytic function on the positive quadrant ${\ell }_{+}^2(\mathbb{N})$ of ${\ell }^2(\mathbb{N})$ and is strictly concave near $0$. As a consequence, the differential of $H^{\ast }$ defines a local diffeomorphism near $0$ of ${\ell }_{\mathbb{C}}^2(\mathbb{N})$.

48 pages

References in corpus (1)

• On Two-Sided Estimates for the Nonlinear Fourier Transform of KdV

Cited by in corpus (2)

• Reducibility for a fast driven linear Klein-Gordon equation
• Tame majorant analyticity for the Birkhoff map of the defocusing Nonlinear Schrödinger equation on the circle