New symplectic structure for KdV

Details New symplectic structure for KdV New symplectic structure for KdV

2000-11-08

arxiv.org/abs/hep-th/0011052v1

Physics

High Energy Physics

High Energy Physics - Theory

To be published in "Integrable Hierarchies and Modern Physics Theories, NATO ARW-UIC 2000" Editors H. Aratyn and A. Sorin

Scientific paper

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.

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