Hamiltonian Structure of the Higher-Order Corrections to the Korteweg-de Vries Equation
- 28 October 1985
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 55 (18) , 1809-1811
- https://doi.org/10.1103/physrevlett.55.1809
Abstract
Higher-order corrections to the Korteweg-de Vries equation are examined by Hamiltonian methods. Starting from the underlying Hamiltonian systems (e.g., the two-fluid equations in the case of ion-acoustic waves), one finds that the corrected equations have the same Poisson bracket as the Korteweg-de Vries equation at every order. One also finds that the underlying equations become nonlocal at sufficiently high order.Keywords
This publication has 13 references indexed in Scilit:
- On integrable systems with higher order correctionsPhysics Letters A, 1985
- Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal MagnetohydrodynamicsPhysical Review Letters, 1980
- Experiments on strong interactions between solitary wavesJournal of Fluid Mechanics, 1978
- The Korteweg-de Vries equation and water waves. Part 3. Oscillatory wavesJournal of Fluid Mechanics, 1978
- Ion-acoustic solitons excited by a single gripJournal of Plasma Physics, 1975
- The Korteweg-de Vries equation and water waves. Part 2. Comparison with experimentsJournal of Fluid Mechanics, 1974
- Experiments on ion-acoustic solitary wavesPhysics of Fluids, 1973
- Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian SystemJournal of Mathematical Physics, 1971
- Canonical transformations depending on a small parameterCelestial Mechanics and Dynamical Astronomy, 1969
- Propagation of Ion-Acoustic Solitary Waves of Small AmplitudePhysical Review Letters, 1966