Hirota polynomials for the KP and BKP hierarchies (Q1311010)

One of the remarkable consequences of the Sato theory of integrable partial differential equations is the role of representation theory in exposing the structure of the solution space. This follows from the action of \(gl(\infty)\) which underlies the theory and the manner in which finite dimensional representations of \(gl(n)\) sit inside it. Thus the solutions reduce to expressions in Schur polynomials and \(Q\)-polynomials. The current paper presents some formulae for the solutions. It must be said that the reader familiar with the work of, for instance, \textit{J. J. C. Nimmo} [J. Phys. A, Math. Gen. 23, No. 5, 751-760 (1990; Zbl 0721.35069)] amongst others, will learn little from the present paper.