On the polynomial τ-functions for the KP hierarchy and the bispectral property

Jorge P. Zubelli

doi:10.1007/BF00430001

On the polynomial τ-functions for the KP hierarchy and the bispectral property

Jorge P. Zubelli

Mathematics

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14 Scopus citations

Abstract

We show that the τ-functions obtained from Schur polynomials lead to wave functions w(x₁, x₂, ... ; k) that possess the following bispectral property: There exists a differential operator B{k,∂_k}, independent of x₁, such that B{k,∂_k}w = Θ {x₁}w, where {x₁} is independent of k. This extends for the KP hierarchy some earlier results of J. J. Duistermaat and F. A. Grünbaum for the rational solutions of KdV and of P. Wright for certain rational solutions of the generalized KdV equations.

Original language	British English
Pages (from-to)	41-48
Number of pages	8
Journal	Letters in Mathematical Physics
Volume	24
Issue number	1
DOIs	https://doi.org/10.1007/BF00430001
State	Published - Jan 1992

Keywords

Mathematics Subject Classifications (1991): 34L25, 35Q51, 35Q52

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10.1007/BF00430001

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AB - We show that the τ-functions obtained from Schur polynomials lead to wave functions w(x1, x2, ... ; k) that possess the following bispectral property: There exists a differential operator B{k,∂k}, independent of x1, such that B{k,∂k}w = Θ {x1}w, where {x1} is independent of k. This extends for the KP hierarchy some earlier results of J. J. Duistermaat and F. A. Grünbaum for the rational solutions of KdV and of P. Wright for certain rational solutions of the generalized KdV equations.

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JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 1

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On the polynomial τ-functions for the KP hierarchy and the bispectral property

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Keywords

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