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Equations of the Camassa-Holm Hierarchy
Rossen I. Ivanov
The squared eigenfunctions of the spectral problem associated with the Camassa-Holm (CH) equation represent a complete basis of functions, which helps to describe the inverse scatt…
Algebraic Discretization of the Camassa-Holm and Hunter-Saxton Equations
Rossen I. Ivanov
The Camassa-Holm (CH) and Hunter-Saxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the and right…
Generalised Fourier Transform and Perturbations to Soliton Equations
Georgi G. Grahovski, Rossen I. Ivanov
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 invol…
Conformal and geometric properties of the Camassa-Holm hierarchy
Rossen I. Ivanov
Integrable equations with second order Lax pair like KdV and Camassa-Holm (CH) exhibit interesting conformal properties and can be written in terms of the so-called conformal invar…