Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy

Strachan, I. A.B. and Zuo, D. (2015) Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy. Journal of Mathematical Physics, 56(11), 113509. (doi: 10.1063/1.4935936)

Abstract

We introduce a Frobenius algebra-valued Kadomtsev-Petviashvili (KP) hierarchy and show the existence of Frobenius algebra-valued τ-function for this hierarchy. In addition, we construct its Hamiltonian structures by using the Adler-Dickey-Gelfand method. As a byproduct of these constructions, we show that the coupled KP hierarchy, defined by Casati and Ortenzi [J. Geom. Phys. 56, 418-449 (2006)], has at least n-“basic” different local bi-Hamiltonian structures. Finally, via the construction of the second Hamiltonian structures, we obtain some local matrix, or Frobenius algebra-valued, generalizations of classical W-algebras.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Zuo, Dr Dafeng and Strachan, Professor Ian
• Authors: Strachan, I. A.B., and Zuo, D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics; College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Mathematical Physics
• Publisher: A I P Publishing
• ISSN: 0022-2488
• ISSN (Online): 1089-7658
• Copyright Holders: Copyright © 2015 AIP Publishing LLC
• First Published: First published in Journal of Mathematical Physics 56(11):113509
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher