On the convexity of the KdV Hamiltonian

DOI10.1007/s00220-015-2563-xzbMath1353.35251arXiv1502.05857OpenAlexW3104784528WikidataQ59888201 ScholiaQ59888201MaRDI QIDQ739571

Alberto Maspero, Peter J. Topalov, Jan-Cornelius Molnar, Thomas Kappeler

Publication date: 18 August 2016

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.05857

zbMATH Keywords

Birkhoff coordinatesKdVaction variables

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Sturm-Liouville theory (34B24)

Related Items (6)

On the Benjamin-Ono equation on \(\mathbb{T}\) and its periodic and quasiperiodic solutions ⋮ Tame majorant analyticity for the Birkhoff map of the defocusing nonlinear Schrödinger equation on the circle ⋮ Small amplitude weak almost periodic solutions for the 1d NLS ⋮ Strong nonlinear instability and growth of Sobolev norms near quasiperiodic finite gap tori for the 2D cubic NLS equation ⋮ On the wellposedness of the KdV equation on the space of pseudomeasures ⋮ Reducibility for a fast-driven linear Klein-Gordon Equation

Cites Work

• On two-sided estimates for the nonlinear Fourier transform of KdV
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• On the parametrization of finite-gap solutions by frequency and wavenumber vectors and a theorem of I. Krichever
• The defocusing NLS equation and its normal form
• Birkhoff coordinates for KdV on phase spaces of distributions
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• The KdV equation under periodic boundary conditions and its perturbations
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• Instability zones of periodic 1-dimensional Schrödinger and Dirac operators
• On the symplectic phase space of K\lowercase{d}V
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