The Generalised Zakharov-Shabat System and the Gauge Group Action
arXiv:1109.5108 · doi:10.1063/1.4732512
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.
17 pages, 1 figure, LaTeX. arXiv admin note: substantial text overlap with arXiv:0710.3302
References in corpus (5)
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