The complex sine-Gordon equation as a symmetry flow of the AKNS hierarchy

Citation
H. Aratyn et al., The complex sine-Gordon equation as a symmetry flow of the AKNS hierarchy, J PHYS A, 33(35), 2000, pp. L331-L337
Citations number
30
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
33
Issue
35
Year of publication
2000
Pages
L331 - L337
Database
ISI
SICI code
0305-4470(20000908)33:35<L331:TCSEAA>2.0.ZU;2-1
Abstract
It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the 'negative' sym metry flows forming the Borel loop algebra. The complex sine-Gordon and the vector nonlinear Schrodinger equations appear as lowest-negative and secon d-positive flows within the extended hierarchy. This is fully analogous to the well known connection between the sine-Gordon and mKdV equations within the extended mKdV hierarchy. A general formalism for a Toda-like symmetry occupying the 'negative' sector of the sl(N) constrained KP hierarchy and g iving rise to the negative Borel sl(N) loop algebra is indicated.