Abstract
The introduction of squared eigenfunctions generates the constrained KP hierarchy and further the extended KP hierarchy. The constrained KP flows constitute a reduced KP hierarchy but the extended KP flows generalize the KP hierarchy. A natural question is when the extended KP flows commute with each other. We aim to analyze this commutativity problem in the extended KP case, and explore the compatibility equations of the extended KP flows. Lax representations of the resulting compatibility equations involve two pseudo-differential operators. We illustrate all the results by a few particular examples, with their Lax pairs being computed.