2000/11/08 by Y. Nutku, Nutku, Y.
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Control and Stability of Dynamical Systems #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Magnetism in coordination complexes #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0011052
To be published in "Integrable Hierarchies and Modern Physics Theories, NATO ARW-UIC 2000" Editors H. Aratyn and A. Sorin
arxiv created 2000/11/08 · openalex publication_date 2000/11/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Starting with Lagrangians, which turn out to be degenerate, the Hamiltonian operators for integrable systems can be constructed using Dirac's theory of constraints. We illustrate this by giving a systematic discussion of the first Hamiltonian structure of KdV. The first symplectic 2-form obtained from Dirac's theory is the time component of the covariant Witten-Zuckerman symplectic 2-form current. We derive the flux of the first symplectic 2-form. Then we turn to a new Lagrangian for KdV recently obtained by Pavlov and present the corresponding new covariant symplectic structure for KdV. This shows that the inverse of Magri's second Hamiltonian operator is also a Hamiltonian operator for KdV.