On the constrained KP hierarchy

Abstract

An explanation for the so-called constrained hierarhies is presented by linking them with the symmetries of the KP hierarchy. While the existence of ordinary symmetries (belonging to the hierarchy) allows one to reduce the KP hierarchy to the KdV hierarchies, the existence of additional symmetries allows to reduce KP to the constrained KP.

7pp, LaTeX

References in corpus (3)

• On Two-Current Realization of KP Hierarchy
• Multi-field representations of KP hierarchies and multi-matrix models
• On The Hamiltonian Structures and The Reductions of The KP Hierarchy

Cited by in corpus (16)

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• Generalized Darboux transformations for the KP equation with self-consistent sources
• On the BKP hierarchy: additional symmetries, Fay identity and Adler-Shiota-van Moerbeke formula
• A new extended KP hierarchy
• Dispersionful analogues of Benney's equations and $N$-wave systems
• A new constrained mKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources
• On the constrained KP hierarchy II
• Constrained KP Models as Integrable Matrix Hierarchies
• Extensions of the matrix Gelfand-Dickey hierarchy from generalized Drinfeld-Sokolov reduction
• Bäcklund transformations for the constrained dispersionless hierarchies and dispersionless hierarchies with self-consistent sources
• A new multi-component two dimensional Toda lattice hierarchy and two dimensional Toda lattice with self-consistent sources
• Solitons from Dressing in an Algebraic Approach to the Constrained KP Hierarchy
• Toda lattice realization of integrable hierarchies
• Matrix Formulation of Hamiltonian Structures of Constrained KP Hierarchy
• The Hamiltonian Structure of Soliton Equations and Deformed W-Algebras
• Extended matrix Gelfand-Dickey hierarchies: reduction to classical Lie algebras