Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
Pure mathematics, Applied mathematics
Abstract
The generalized Zakharov-Shabat systems with complex-valued non-regular Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studied. This study includes: the properties of fundamental analytical solutions (FAS) for the gauge-equivalent to CBC systems and the minimal set of scattering data; the description of the class of nonlinear evolutionary equations, solvable by the inverse scattering method, and the recursion operator, related to such systems; the hierarchies of Hamiltonian structures. The results are illustrated on the example of the multi-component nonlinear Schrodinger (MNLS) equations and the corresponding gauge-equivalent multi-component Heisenberg ferromagnetic (MHF) type models, related to so(5;C) algebra.
DOI
https://doi.org/10.1063/1.4732512
Recommended Citation
Grahovski, G. (2012). The Generalised Zakharov-Shabat System and the Gauge Group Action Journal of Mathematical Physics, vol. 53, 073512. doi:10.1063/1.4732512
Included in
Mathematics Commons, Non-linear Dynamics Commons, Ordinary Differential Equations and Applied Dynamics Commons, Partial Differential Equations Commons
Publication Details
Journal of mathematical physics. 53 (2012), 073512
Published online.
(E-print: arXiv1109.5108)