A perturbation theory for the Korteweg-de Vries equation

By writing the perturbed Korteweg-de Vries equation in operator form, equations are derived which are a basis for a perturbation method. In particular, in the first approximation, the authors obtain from them equations describing the evolution of the soliton amplitude and velocity. The present theory may be extended, also, to other nonlinear evolution equations if they are solved, without perturbation, by the inverse-problem method. (Auth.)