Japanese Journal of Mathematics

, Volume 13, Issue 2, pp 235–271 | Cite as

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

  • Victor G. KacEmail author
  • Johan W. van de Leur
Special Feature: The Takagi Lectures


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 and phrases

KP and MKP hierarchies tau-functions wave functions formal pseudo-differential operators Schur polynomials 

Mathematics Subject Classification (2010)

14M15 17B10 17B65 17B67 20G43 22E70 35Q53 35R03 47G30 


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Copyright information

© The Mathematical Society of Japan and Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Mathematical InstituteUtrecht UniversityUtrechtThe Netherlands

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