Generalised Fourier transform and perturbations to soliton equations
Georgi Grahovski - School of Electronic Engineering, Dublin City University, Glasnevin, Dublin 9, Ireland (email)
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.
Keywords: Inverse Scattering Method, Soliton Perturbations, KdV equation, Camassa-Holm equation, Ostrovsky equation.
Received: May 2009; Revised: June 2009; Published: July 2009.
2011 Impact Factor.921