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arXiv · 1109.5108

The Generalised Zakharov-Shabat System and the Gauge Group Action

Georgi G. Grahovski
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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.

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BibTeXRIS

Georgi G. Grahovski. 2012-07-21. The Generalised Zakharov-Shabat System and the Gauge Group Action. https://doi.org/10.1063/1.4732512

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