Classes of third order non-Abelian evolution equations linked to that of Korteweg-de Vries-type are investigated and their connections represented in a non-commutative Bäcklund chart, generalizing results in [Fuchssteiner B., Carillo S., Phys. A 154 (1989), 467-510]. The recursion operators are shown to be hereditary, thereby allowing the results to be extended to hierarchies. The present study is devoted to operator nonlinear evolution equations: general results are presented. The implied applications referring to finite-dimensional cases will be considered separately.
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机译：研究了与Korteweg-de Vries型方程相联系的三阶非阿贝尔演化方程的类，并用非交换Bäcklund图表表示了它们的联系，并将结果推广到[Fuchssteiner B.，Carillo S.，Phys。 A 154（1989），467-510]。递归运算符显示为遗传的，因此可以将结果扩展到层次结构。本研究致力于算子非线性演化方程：给出了一般结果。涉及有限维情况的隐含应用程序将单独考虑。
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