Exploring the connection between quasistationary and squared eigenfunction expansion techniques in soliton perturbation theory

Abstract

We give a short review of the techniques that have been used to study soliton perturbations for nonlinear integrable systems in 1 + 1 dimensions. In particular, we discuss the connection between direct perturbation methods using squared eigenfunction expansions and quasistationary perturbation theory. We show for the KdV (Korteweg–de Vries) how the results for quasistationary approximations are related to those for the standard adiabatic perturbation theory.