Poisson brackets for Lagrangians linear in the velocity
type: Item
instance of: scholarly article
title: Poisson brackets for Lagrangians linear in the velocity
zbMATH Open document ID: 0598.58024
DOI: 10.1007/BF00704581
author: E. A. De Kerf
author: Maarten Bergvelt
published in: Letters in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: The authors derive the Poisson bracket \[ \{g,h\}[u]=\int dx\frac{\delta g}{\delta u(x)}\frac{\partial}{\partial x}\frac{\delta h}{\delta u(x)} \] with g and h functionals of u(x), using the symplectic formulation of mechanics described, for example, in the book by \textit{R. Abraham} and \textit{J. E. Marsden} [Foundations of mechanics: 2nd ed. (1978; Zbl 0393.70001)]. The Korteweg-de Vries equation and the time-dependent Schrödinger equation are used as examples to illustrate the procedure.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 3965032
zbMATH Keywords: hamiltonian
zbMATH Keywords: Poisson bracket
zbMATH Keywords: time-dependent Schrödinger equation
MaRDI profile type: Publication
cites work: Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian System
cites work: Presymplectic manifolds and the Dirac–Bergmann theory of constraints
cites work: Q4724559
cites work: The Hamiltonian structure associated to evolution-type Lagrangians
cites work: On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
full work available at URL: https://doi.org/10.1007/bf00704581
OpenAlex ID: W2001618980
description: scientific article; zbMATH DE number 3965032