A relationship between rational and multi-soliton solutions of the BKP hierarchy
| dc.creator | Nimmo, J. J. C. | |
| dc.creator | Orlov, A. Yu. | |
| dc.date | 2004-05-06 | |
| dc.date.accessioned | 2026-07-07T05:35:31Z | |
| dc.date.available | 2026-07-07T05:35:31Z | |
| dc.description | 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 $ξ(k)$, $k\in\mathbb{Z^+}$, 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 $ξ(k)$ 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. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/nlin/0405009 | |
| dc.identifier | http://arxiv.org/abs/nlin/0405009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80722 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | A relationship between rational and multi-soliton solutions of the BKP hierarchy | |
| dc.type | text |