Weakly and strongly coupled intermediate long-wave hierarchies and Benjamin-Ono equations

摘要

In this paper, we construct weakly and strongly coupled intermediate long-wave (ILW) hierarchies which contain integrable weakly (strongly) coupled Benjamin-Ono(2) equations as the primary equations. The dressing operators Phi(+/-) 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.