Vertex Operators and Solitons of Constrained KP Hierarchies

Details Vertex Operators and Solitons of Constrained KP Hierarchies Vertex Operators and Solitons of Constrained KP Hierarchies

1997-11-20

arxiv.org/abs/solv-int/9711011v1

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, needs lamuphys.tex and lamuphys.sty, talk presented at the 1997 UIC Workshop on Supersymmetry and Integrable Models,

Scientific paper

10.1007/BFb0105320

We construct the vertex operator representation for the Affine Kac-Moody $SL(M+K+1)$ algebra, which is relevant for the construction of the soliton solutions of the constrained KP hierarchies. The oscillators involved in the vertex operator construction are provided by the Heisenberg subalgebras of $SL(M+K+1)$ realized in the unconventional gradations. The well-known limiting cases are the homogeneous Heisenberg subalgebra of $SL(M+1)$ and the principal Heisenberg subalgebra of ${\hat{sl}}(K+1)$. The explicit example of $M=K=1$ is discussed in detail and the corresponding soliton solutions and tau-functions are given.

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