Abstract
We consider an auxiliary linear problem on the algebra sl(3) with reductions of ℤ2 × ℤ2 type introduced recently by Gerdjikov, Mikhailov and Valchev (GMV), and discuss its relation with a Generalized Zakharov-Shabat system having the same type of reduction symmetry. We describe the gauge-equivalent hierarchies and find explicitly the analog of the first nontrivial soliton equation in the hierarchy of equations related to GMV linear problem.
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