Involutive functionals, infinite dimensional tori, and neighboring tori

DOI10.1006/jfan.1997.3169zbMath0913.58026OpenAlexW1993140013MaRDI QIDQ1270007

Martin jun. Schwarz

Publication date: 26 May 1999

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1997.3169

zbMATH Keywords

infinite dimensional toriinfinite dimensional version of the Liouville theoreminvolutive functionalsneighbouring tori

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Almost and pseudo-almost periodic solutions to PDEs (35B15) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Cites Work

• The initial value problem for the sequence of generalized Korteweg-de Vries equations
• Commuting flows and invariant tori: Korteweg-de Vries
• The periodic problem for the Korteweg-de Vries equation
• Hill's operator with finitely many gaps
• The spectrum of Hill's equation
• Periodic solutions of the KdV equation
• Almost Periodic Solutions of the KdV Equation
• Hill's operator and hyperelliptic function theory in the presence of infinitely many branch points
• Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
• Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian System
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