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arXiv · hep-th/9308137

The $n$-component KP hierarchy and representation theory

V. G. Kac·J. W. van de Leur
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Abstract

Starting from free charged fermions we give equivalent definitions of the $n\/$-component KP hierarchy, in terms of $τ\/$-functions $τ_α\/$ (where $α\in M =\/$ root lattice of $sl_n\/$), in terms of $n \times n\/$ matrix valued wave functions $W_α(α\in M)\/$, and in terms of pseudodifferential wave operators $P_α(α\in M)\/$. These imply the deformation and the zero curvature equations. We show that the 2-component KP hierarchy contains the Davey-Stewartson system and the $n\geq3\/$ component KP hierarchy continues the $n\/$-wave interaction equations. This allows us to construct theis solutions.

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V. G. Kac, J. W. van de Leur. 1993-09-01. The $n$-component KP hierarchy and representation theory. https://doi.org/10.1063/1.1590055

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