Four examples of the inverse method as a canonical transformation
- 1 January 1975
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 16 (1) , 96-99
- https://doi.org/10.1063/1.522391
Abstract
The Toda lattice, the nonlinear Schrödinger equation, the sine−Gordon equation, and the Korteweg−de Vries equation are four nonlinear equations of physical importance which have recently been solved by the inverse method. For these examples, this method of solution is interpreted as a canonical transformation from the initial Hamiltonian dynamics to an ’’action−angle’’ form. This canonical structure clarifies the independence of an infinite number of constants of the motion and indicates the special nature of the solution by the inverse method.Keywords
This publication has 7 references indexed in Scilit:
- On the Toda Lattice. II: Inverse-Scattering SolutionProgress of Theoretical Physics, 1974
- The Toda lattice. II. Existence of integralsPhysical Review B, 1974
- Nonlinear-Evolution Equations of Physical SignificancePhysical Review Letters, 1973
- The soliton: A new concept in applied scienceProceedings of the IEEE, 1973
- Korteweg-de Vries equation: A completely integrable Hamiltonian systemFunctional Analysis and Its Applications, 1972
- Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian SystemJournal of Mathematical Physics, 1971
- Method for Solving the Korteweg-deVries EquationPhysical Review Letters, 1967