Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian System
- 1 August 1971
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 12 (8) , 1548-1551
- https://doi.org/10.1063/1.1665772
Abstract
It is shown that if a function of x and t satisfies the Korteweg‐de Vries equation and is periodic in x, then its Fourier components satisfy a Hamiltonian system of ordinary differential equations. The associated Poisson bracket is a bilinear antisymmetric operator on functionals. On a suitably restricted space of functionals, this operator satisfies the Jacobi identity. It is shown that any two of the integral invariants discussed in Paper II of this series have a zero Poisson bracket.Keywords
This publication has 2 references indexed in Scilit:
- Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of MotionJournal of Mathematical Physics, 1968
- Non-linear dispersive wavesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1965