Hirota polynomials for the KP and BKP hierarchies
type: Item
instance of: scholarly article
title: Hirota polynomials for the KP and BKP hierarchies
zbMATH Open document ID: 0807.35122
DOI: 10.1007/BF00760859
author: C. M. Yung
author: T. H. Baker
author: Peter D Jarvis
published in: Letters in Mathematical Physics
publication date: 1994-01-26T00:00:00Z
review text: One of the remarkable consequences of the Sato theory of integrable partial differential equations is the role of representation theory in exposing the structure of the solution space. This follows from the action of \(gl(\infty)\) which underlies the theory and the manner in which finite dimensional representations of \(gl(n)\) sit inside it. Thus the solutions reduce to expressions in Schur polynomials and \(Q\)-polynomials. The current paper presents some formulae for the solutions. It must be said that the reader familiar with the work of, for instance, \textit{J. J. C. Nimmo} [J. Phys. A, Math. Gen. 23, No. 5, 751-760 (1990; Zbl 0721.35069)] amongst others, will learn little from the present paper.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 484126
zbMATH Keywords: Schur functions
zbMATH Keywords: \(Q\)-functions
zbMATH Keywords: Kadomtsev-Petviashvili equation
reviewed by: Christopher Athorne
MaRDI profile type: Publication
cites work: Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–
cites work: Solitons and infinite dimensional Lie algebras
cites work: Q4011449
cites work: Hall-Littlewood symmetric functions and the BKP equation
cites work: Q3947818
cites work: Symmetric functions and the KP and BKP hierarchies
cites work: The Schur function realization of vertex operators
cites work: Wronskian determinants, the KP hierarchy and supersymmetric polynomials
cites work: A Determinantal Formula for Skew Q -Functions
description: scientific article; zbMATH DE number 484126