Victor Kac, Johan van de Leur
Published 2018-01-09Version 1
We give 4 formulations of the Modified KP hierarchy and show that they are equivalent. We also discuss the reductions of the MKP hierarchy to the modified $n$-KdV hierarchies. As a byproduct, we find an astonishingly simple explicit description of all polynomial tau-functions of the KP, the MKP and the $n$-KdV hierarchies, and (implicitly) also for the modified $n$-KdV hierarchy.
On tau-functions for the KdV hierarchy
Polynomial tau-functions for the multi-component KP hierarchy
Galilean symmetry of the KdV hierarchy
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