Periodic and almost-periodic potentials in inverse problems

Authors
Krichever, I Novikov, SP
Citation
I. Krichever et Sp. Novikov, Periodic and almost-periodic potentials in inverse problems, INVERSE PR, 15(6), 1999, pp. R117-R144
Citations number
89
Categorie Soggetti
Physics
Journal title
INVERSE PROBLEMS
ISSN journal
02665611 → ACNP
Volume
15
Issue
6
Year of publication
1999
Pages
R117 - R144
Database
ISI
SICI code
0266-5611(199912)15:6<R117:PAAPII>2.0.ZU;2-Q
Abstract
An updated and detailed survey of basic ideas of the finite-gap theory is p resented. That theory, developed to construct periodic and quasi-periodic s olutions of the soliton equations, combines the Bloch-Floquet spectral theo ry of linear periodic operators, the theory of completely integrable Hamilt onian systems, the classical theory of Riemann surfaces, and theta-function s.