The n-component KP hierarchy and representation theory

1993/08/31 by V. G. Kac, J. W. van de Leur · 2 citations
Physics and Astronomy · #hep-th

paper · pdf · doi:10.1063/1.1590055

published as J.Math.Phys. 44 (2003) 3245-3293

arxiv created 1993/09/01 · arxiv updated 2009/11/30

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∈ M =\/ root lattice of sl_n\/), in terms of n × n\/ matrix valued wave functions W_α(α∈ M)\/, and in terms of pseudodifferential wave operators P_α(α∈ 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≥3\/ component KP hierarchy continues the n\/-wave interaction equations. This allows us to construct theis solutions.

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