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

✍ Scribed by Jorge P. Zubelli

Publisher
Springer
Year
1992
Tongue
English
Weight
317 KB
Volume
24
Category
Article
ISSN
0377-9017

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✦ Synopsis

We show that the z-functions obtained from Schur polynomials lead to wave functions w(x~, x 2 . . . . ;k) that possess the following bispectral property: There exists a differential operator B(k, Ok), independent of xl, such that B(k, #k)W =O(Xl)W, where | is independent of k. This extends for the KP h~erarchy some earlier results of J. J. Duistermaat and F. A. Grfinbaum for the rational solutions of KdV and of P. Wright for certain rational solutions of the generalized KdV equations.

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