Affine Lie algebraic origin of constrained KP hierarchies

DOI10.1063/1.530970zbMath0842.35098arXivhep-th/9408104OpenAlexW3100468574MaRDI QIDQ4873503

A. H. Zimerman, J. F. Gomes, Henrik Aratyn

Publication date: 5 May 1996

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9408104

zbMATH Keywords

constrained KP hierarchyLax formulationToda lattice structuregeneralized nonlinear Schrödinger hierarchymulti-boson KP-Toda hierarchies

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (12)

The Hamiltonian structure of the \(N=2\) supersymmetric GNLS hierarchy. ⋮ Constrained KP models as integrable matrix hierarchies ⋮ Solving the constrained KP hierarchy by gauge transformations ⋮ Darboux-Bäcklund solutions of \(\text{SL}(p,q)\) KP-KdV hierarchies, constrained generalized Toda lattices, and two-matrix string model ⋮ Some comments on the bi(tri)-Hamiltonian structure of generalized AKNS and DNLS hierarchies ⋮ Multicomponent Fokas–Lenells equations on Hermitian symmetric spaces ⋮ Hierarchies of evolution equations associated with certain symmetric spaces ⋮ Matrix formulation of Hamiltonian structures of constrained KP hierarchy ⋮ A Vector Fokas-Lenells System from the Coupled Nonlinear Schrödinger Equations ⋮ Zero Curvature Formalism for Supersymmetric Integrable Hierarchies in Superspace ⋮ Generalized Bäcklund transformations for affine Toda hierarchies ⋮ Integrable hierarchy for multidimensional Toda equations and topological-anti-topological fusion.

Cites Work

• Nonlinear Schrödinger equations and simple Lie algebras
• Kac-Moody symmetry of generalized nonlinear Schrödinger equations
• Kac-Moody Lie algebras and soliton equations. II: Lax equations associated with \(A_ 1^{(1)}\)
• Multi-field representations of the KP hierarchy and multi-matrix models
• Systems of Toda type, inverse spectral problems, and representation theory
• Solving the KP hierarchy by gauge transformations
• Constrained KP hierarchy and bi-Hamiltonian structures
• Darboux theorems and Wronskian formulas for integrable systems. I: Constrained KP flows
• On two-current realization of KP hierarchy
• Exact solubility of Chern-Simons theory with compact simple gauge group
• Mathematics of dispersive water waves
• τ functions and zero curvature equations of Toda–AKNS type
• Commuting flows and conservation laws for Lax equations
• New reductions of the Kadomtsev–Petviashvili and two-dimensional Toda lattice hierarchies via symmetry constraints
• Constraints of the Kadomtsev–Petviashvili hierarchy
• GAUGE TRANSFORMATIONS AND RECIPROCAL LINKS IN 2 + 1 DIMENSIONS
• Matrix nonlinear Schrödinger equations and moment maps into loop algebras

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