On the Caudrey-Beals-Coifman System and the Gauge Group Action

The generalized Zakharov-Shabat systems with complex-valued Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studies. This 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.

💡 Research Summary

The paper presents a comprehensive study of generalized Zakharov‑Shabat (ZS) systems that incorporate complex‑valued Cartan elements, the class of systems originally introduced by Caudrey, Beals and Coifman (CBC systems), and the gauge‑equivalent formulations that connect the two frameworks. The authors begin by formulating the Lax operator
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