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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 Schr¨odinger (MNLS) equations and the corresponding gauge-equivalent multi-component Heisenberg ferromagnetic (MHF) type models, related to so(5,C) algebra.
G. Grahovski, The generalised Zakharov-Shabat system and the gauge group action, J. Math. Phys., Volume 53, Issue 7, pp. 073512-073512-13 (2012). doi : 10.21427/p4k0-gq64