Theory of canonical transformations for nonlinear evolution equations. I., II. (Q2749972)

From the summaries: In the first paper we investigate a canonical transformation for nonlinear evolution equations which keeps the Hamiltonian form invariant. It is shown that the so-called Bäcklund transformation is the canonical transformation of this type. The group property of the canonical transformation and relations between infinitesimal canonical transformations and conservation laws are also investigated. The sine-Gordon equation, Korteweg-de Vries equation and modified Korteweg-de Vries equation are considered as examples. In the second paper, canonical transformations for nonlinear evolution equations are discussed in relation to the inverse scattering scheme and conservation laws.