Vertex Operators and Solitons of Constrained KP Hierarchies

Abstract

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 $\widehat{sl}(K+1)$. The explicit example of $M=K=1$ is discussed in detail and the corresponding soliton solutions and tau-functions are given.

13 pages, needs lamuphys.tex and lamuphys.sty, talk presented at the 1997 UIC Workshop on Supersymmetry and Integrable Models, Chicago, USA, June/97. To be published in Lecture Notes in Physics, Springer-Verlag

References in corpus (3)

• Tau-functions and Dressing Transformations for Zero-Curvature Affine Integrable Equations
• Constrained KP Models as Integrable Matrix Hierarchies
• Solitons from Dressing in an Algebraic Approach to the Constrained KP Hierarchy

Cited by in corpus (1)

• Supersymmetry and the KdV equations for Integrable Hierarchies with a Half-integer Gradation