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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics