The perturbed Korteweg-de Vries equation considered anew

The perturbed Korteweg-de Vries equation is studied in a new way by a Green's function formalism without use of inverse scattering methods. The Green's function is determined by employing the Backlund transformation and Green's theorem. After a thorough analysis of the exact first-order solution with regard to secular terms, a two-time scale expansion leads to the adiabatic approximation and the first-order correction, in accordance with the results of Karpman and Maslov. Contrary to statements in the literature, the term tanh(2)z in the expression for the modified phase of the perturbed soliton arises as a consequence of the systemstically conducted first-order perturbation theory. (C) 1997 American Institute of Physics.