Abstract
One of the ways to overcome existing limitations of the famous Wahlquist-Estabrook procedure consists in employing normal forms of zero curvature representations (ZCR). While in case of sľ 2 normal forms are known for a long time, the next step is made in this paper. We find normal forms of sľ 3 -valued ZCR that are not reducible to a proper subalgebra of sľ 3 . We also prove a reducibility theorem, which says that if one of the matrices in a ZCR ( A, B ) falls into a proper subalgebra of sľ 3 , then the second matrix either falls into the same subalgebra or the ZCR is in a sense trivial. In the end of this paper we show examples of ZCR and their normal forms.
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