Abstract
We consider evolution systems admitting L-A-pairs in ℤ-graded Lie algebras. We relate several hierarchies of integrable systems to a single L operator. The different hierarchies corresponds to different decompositions of the zero component of a ℤ-graded algebra into the sum of two subalgebras. This allows us to construct new examples of multi-component integrable system following the Burgers, mKdV, NLS and Boussinesq equations.
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