Hall-Littlewood symmetric functions and the BKP equation

Abstract

The connection between solutions of the BKP equation and Hall-Littlewood symmetric functions is utilised in a unified approach to soliton and polynomial solutions. This is analogous to the Wronskian formulation of the solution of the KP equation. As a by-product, two novel expressions for certain Hall-Littlewood functions in terms of Pfaffians are derived.