A brief survey of the theory of soliton perturbations is
presented. The focus is on the usefulness of the so-called
Generalised Fourier Transform (GFT). This is a method that
involves expansions over the complete basis of "squared
solutions'' of the spectral problem, associated to the soliton
equation. The Inverse Scattering Transform for the corresponding
hierarchy of soliton equations can be viewed as a GFT where the
expansions of the solutions have generalised Fourier coefficients
given by the scattering data.
The GFT provides a natural setting for the analysis of small
perturbations to an integrable equation: starting from a purely
soliton solution one can 'modify' the soliton parameters such as
to incorporate the changes caused by the perturbation.
As illustrative examples the perturbed equations of the KdV
hierarchy, in particular the Ostrovsky equation, followed by the
perturbation theory for the Camassa-Holm hierarchy are presented.