Abstract
This work is dedicated to some notes on the Moyal momentum algebras applied to the sl_3 Boussinesq integrable hierarchy. Starting from a brief review of the Moyal momentum algebra structures, we establish in detail the Non-commutative Boussinesq hierarchy by using the Lax pair Generating Technique. Then we shows that these equations can be obtained as 3-reduction of Non-commutative KP hierarchy in a similarly form via some conformal realizations.
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