A geometric interpretation of the spectral problem for the generalized sine-Gordon system

Authors
Cieslinski, JL Aminov, YA
Citation
Jl. Cieslinski et Ya. Aminov, A geometric interpretation of the spectral problem for the generalized sine-Gordon system, J PHYS A, 34(13), 2001, pp. L153-L159
Citations number
32
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
34
Issue
13
Year of publication
2001
Pages
L153 - L159
Database
ISI
SICI code
0305-4470(20010406)34:13<L153:AGIOTS>2.0.ZU;2-8
Abstract
The generalized sine-Gordon system is an integrable system implicitly descr ibing submanifolds of negative constant curvature in Euclidean spaces. To o btain the associated spectral problem we consider immersions of these subma nifolds in spheres. The spectral parameter turns out to be related to the r adius of the spheres. We also derive the so-called Sym-Tafel formula which yields the radius vector of negative constant curvature submanifolds in Euc lidean spaces.