Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions
Name
1801.02845.pdf
Description
Submitted version
Size
320.5 KB
Format
Adobe PDF
Checksum (MD5)
07c47c4aa8ae464030f8cd50a4f15086
Author(s)
Kac, Victor
van de Leur, Johan W.
Date Issued
July 2018
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
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
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s11537-018-1803-1
