Nimmo, J.J.C. and Orlov, A.Y. (2005) A relationship between rational and multi-soliton solutions of the BKP hierarchy. Glasgow Mathematical Journal, 47(A), pp. 149-168.
Text
13239.pdf 197kB |
Publisher's URL: http://dx.doi.org/10.1017/S0017089505002363
Abstract
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 $\xi(k)$, $k\in\mathbb{Z^+}$, 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 $\xi(k)$ 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.
Item Type: | Articles |
---|---|
Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Nimmo, Dr Jonathan |
Authors: | Nimmo, J.J.C., and Orlov, A.Y. |
Subjects: | Q Science > QA Mathematics |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Glasgow Mathematical Journal |
Publisher: | Cambridge University Press |
ISSN: | 0017-0895 |
ISSN (Online): | 1469-509X |
Published Online: | 14 July 2005 |
Copyright Holders: | Copyright © 2005 Cambridge University Press |
First Published: | First published in Glasgow Mathematical Journal 47(A):149-168 |
Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher. |
University Staff: Request a correction | Enlighten Editors: Update this record