# CBC Systems with Mikhailov Reductions by Coxeter Automorphism: I. Spectral Theory of the Recursion Operators

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We consider the Caudrey–Beals–Coifman linear problem (CBC problem) and the theory of the Recursion Operators (Generating Operators) related to it in the presence of ${\mathbb{Z}}_{h}$‐reductions of Mikhailov type defined by Coxeter automorphism of the underlying algebra. We discuss mainly the spectral aspects of the theory of the Recursion Operators related to the expansions over the adjoint solutions of the CBC problem but pay attention also to the algebraic issues related to the recursion relations through which the hierarchies of the nonlinear evolution equations associated with the CBC auxiliary problem are obtained.
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Document Type: Research Article

Publication date: February 1, 2015

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