2004/05/06 by J. J. C. Nimmo, Nimmo, J. J. C., A. Yu. Orlov +1
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0405009
15 pages
arxiv created 2004/05/06 · arxiv updated 2009/12/01
We consider a special class of solutions of the BKP hierarchy which we call τ-functions of hypergeometric type. These are series in Schur Q-functions over partitions, with coefficients parameterised by a function of one variable ξ, where the quantities ξ(k), k∈\mathbbZ+, 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 ξ(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 τ-function of hypergeometric type. We also show that the KdV and the NLS soliton τ-functions coinside the BKP τ-functions of hypergeometric type, evaluated at special point of BKP higher time; the variables ξ (which are BKP integrals of motions) being related to KdV and NLS higher times.