Four examples of the inverse method as a canonical transformation

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.