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CATEGORIES:Applied and Computational Analysis
SUMMARY:Inverse scattering for the Camassa-Holm hierarchy
- Rossen Ivanov (Trinity College Dublin and Dublin
Institute of Technology)
DTSTART;TZID=Europe/London:20081016T150000
DTEND;TZID=Europe/London:20081016T160000
UID:TALK14306AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/14306
DESCRIPTION:The inverse scattering method is developed for the
Camassa–Holm equation. As an illustration the so
lutions corresponding to the reflectionless\npoten
tials are constructed in terms of the scattering d
ata. The main difference with respect to the stand
ard inverse scattering transform lies in the fact
that we have a weighted spectral problem. This req
uires different asymptotic expansions for the eige
nfunctions.\n\nThe squared eigenfunctions of the s
pectral problem associated with the\nCamassa–Holm
equation represent a complete basis of functions\,
which helps\nto describe the inverse scattering t
ransform for the Camassa–Holm hierarchy as a gener
alized Fourier transform. There exists a completen
ess relation for the squared solutions of the Cama
ssa–Holm\nspectral problem. We show that all the f
undamental properties of the Camassa–Holm equation
such as the integrals of motion\, the description
of the equations of the whole hierarchy and their
Hamiltonian structures can be naturally expressed
making use of the completeness relation and the r
ecursion operator\, whose eigenfunctions are the s
quared solutions.
LOCATION:MR14\, CMS
CONTACT:
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