Poisson brackets for Lagrangians linear in the velocity
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.
scientific article; zbMATH DE number 3965032