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On Soliton Equations of Exceptional Type

✍ Scribed by S.R. Lu

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
484 KB
Volume
166
Category
Article
ISSN
0021-8693

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✦ Synopsis

The main purpose of this paper is to present an explicit formula for the general hierarchy of soliton equations constructed by Kac-Wakimoto from the basic representation of an arbitrary affine Kac-Moody algebra. The results turn out that the differential operators of the corresponding Hirota bilinear equations can be written explicitly in terms of skew Schur functions for both principal and homogeneous hierarchies. The principal hierarchy includes the classical KP and (\mathrm{KdV}) equations. The homogeneous hierarchy turns out to be related to the classical non-linear SchrΓΆdinger equation for type (A_{1}^{(1)}) and to the classical 2-dimensional Toda lattice equation for type (A_{2}^{(\mathrm{I})}). (C) 1994 Academic Press, Inc.

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