Polynomial tau-functions of the n-th Sawada-Kotera hierarchy

Abstract

We find all polynomial tau-functions of the n-th reduced BKP hierarchy (=n-th Sawada-Kotera hierarchy). The name comes from the fact that for n=3 the simplest equation of the hierarchy is the famous Sawada-Kotera equation.

13 pages, no figures Revised version. There was a mistake in some arguments. We have corrected this. The main Theorem is corrected