Affine Lie Algebraic Origin of Constrained KP Hierarchies

Abstract

We present an affine $sl(n+1)$ algebraic construction of the basic constrained KP hierarchy. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and we show that these approaches are equivalent. The model is recognized to be the generalized non-linear Schrödinger ($\GNLS$) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Bäcklund transformations and interpolate between $\GNLS$ and multi-boson KP-Toda hierarchies. Our construction uncovers origin of the Toda lattice structure behind the latter hierarchy.

25 pgs, LaTeX, IFT-P/029/94 and UICHEP-TH/93-10

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Cited by in corpus (16)

• Constrained KP Models as Integrable Matrix Hierarchies
• Integrable Hierarchy for Multidimensional Toda Equations and Topological-Anti-topological Fusion
• The sAKNS Hierarchy
• Zero Curvature Formalism for Supersymmetric Integrable Hierarchies in Superspace
• The Hamiltonian structure of the N=2 supersymmetric GNLS hierarchy
• Multicomponent Fokas-Lenells equations on Hermitian symmetric spaces
• Symmetries of Supersymmetric Integrable Hierarchies of KP Type
• Solitons from Dressing in an Algebraic Approach to the Constrained KP Hierarchy
• T-Duality in 2-D Integrable Models
• New derivation of soliton solutions to the AKNS${}_2$ system via dressing transformation methods
• Generalized Backlund transformations for Affine Toda Hierarchies
• Vertex Operators and Solitons of Constrained KP Hierarchies
• Some comments on the bi(tri)-Hamiltonian structure of Generalized AKNS and DNLS hierarchies
• Vertex Operators and Soliton Solutions of Affine Toda Model with U(2) Symmetry
• Matrix Formulation of Hamiltonian Structures of Constrained KP Hierarchy
• Susy Hierarchies and Affine Algebras