A RELATIONSHIP BETWEEN RATIONAL AND MULTI-SOLITON SOLUTIONS OF THE BKP HIERARCHY

We consider a special class of solutions of the BKP hierarchy which we call (tau)-functions of hypergeometric type. These are series in Schur Q-functions over partitions, with coefficients parameterised by a function of one variable (xi), where the quantities (xi)(k), k (element of) Z+, are integrals of motion of the BKP hierarchy. We show that this solution is, at the same time, a infinite soliton solution of a dual BKP hierarchy, where the variables (xi)(k) are now related to BKP higher times. In particular, rational solutions of the BKP hierarchy are related to (finite) multi-soliton solution of the dual BKP hierarchy. The momenta of the solitons are given by the parts of partitions in the Schur Q-function expansion of the (tau)-function of hypergeometric type. We also show that the KdV and the NLS soliton (tau)-functions coinside the BKP (tau)-functions of hypergeometric type, evaluated at special point of BKP higher time; the variables (xi) (which are BKP integrals of motions) being related to KdV and NLS higher times.