Theory of Canonical Transformations for Nonlinear Evolution Equations. I

Abstract

For nonlinear evolution equations, a canonical transformation which keeps the Hamiltonian form invariant is investigated. It is shown that the so-called Bäcklund transformation is the canonical transformation of this type. Group property of the canonical transformation and relations between infinitesimal canonical transformations and conservation laws are also investigated. Sine-Gordon equation, Korteweg-de Vries equation and modified Korteweg-de Vries equation are considered as examples.