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

V.G. Kac; J.W. van de Leur

doi:10.1007/s11537-018-1803-1

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

V.G. Kac
, J.W. van de Leur

Massachusetts Institute of Technology

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	235-271
Journal	Japanese Journal of Mathematics
Volume	13
Issue number	2
DOIs	https://doi.org/10.1007/s11537-018-1803-1
Publication status	Published - 2018

Keywords

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

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10.1007/s11537-018-1803-1

kacFinal published version, 685 KBLicence: Taverne

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title = "Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions",

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.",

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AU - Kac, V.G.

AU - van de Leur, J.W.

PY - 2018

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AB - 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.

KW - KP and MKP hierarchies

KW - tau-functions

KW - wave functions

KW - formal pseudo-differential operators

KW - Schur polynomials

U2 - 10.1007/s11537-018-1803-1

DO - 10.1007/s11537-018-1803-1

M3 - Article

SN - 1861-3624

VL - 13

SP - 235

EP - 271

JO - Japanese Journal of Mathematics

JF - Japanese Journal of Mathematics

IS - 2

ER -

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

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