Abstract
In this paper, we construct weakly and strongly coupled intermediate long-wave (ILW) hierarchies which contain integrable weakly (strongly) coupled Benjamin–Ono2 equations as the primary equations. The dressing operators [Formula: see text] of the weakly and strongly coupled ILW hierarchies satisfy the Sato equations of a weakly (strongly) coupled KP hierarchy. We found an infinite system of commuting integrals of motion related to the weakly and strongly coupled Benjamin–Ono integrable hierarchies.
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