Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions

Author(s)
Kac, Victor; van de Leur, Johan W.
Thumbnail
DownloadSubmitted version (320.5Kb)
Terms of use
Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
Metadata
Show full item record
Abstract
We show that a system of Hirota bilinear equations introduced by Jimbo and Miwa defines tau-functions of the modified KP (MKP) hierarchy of evolution equations introduced by Dickey. Some other equivalent definitions of the MKP hierarchy are established. All polynomial tau-functions of the KP and the MKP hierarchies are found. Similar results are obtained for the reduced KP and MKP hierarchies. Keywords: KP and MKP hierarchies; tau-functions; wave functions; formal pseudo-differential operators; Schur polynomials
Date issued
2018-07
URI
https://hdl.handle.net/1721.1/125302
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Japanese Journal of Mathematics
Publisher
Springer Science and Business Media LLC
Citation
Kac, Victor G. and van de Leur, Johan, "Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions." Japanese Journal of Mathematics 13, 2 (September 2018): 235–271. © 2018, The Mathematical Society of Japan and Springer Japan KK.
Version: Original manuscript
ISSN
0289-2316
1861-3624
Collections