The (N,M)th Korteweg–de Vries hierarchy and the associated W-algebra

DOI10.1063/1.530710zbMath0820.35115arXivhep-th/9311070OpenAlexW1541921183WikidataQ64038596 ScholiaQ64038596MaRDI QIDQ4327268

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Publication date: 5 April 1995

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

Full work available at URL: https://arxiv.org/abs/hep-th/9311070

zbMATH Keywords

Poisson structurereductionsKdV hierarchyKP hierarchyLax operatorintegrable hierarchydispersionless limit

Mathematics Subject Classification ID

Virasoro and related algebras (17B68) KdV equations (Korteweg-de Vries equations) (35Q53) Invariance and symmetry properties for PDEs on manifolds (58J70)

Related Items

Higher genera Catalan numbers and Hirota equations for extended nonlinear Schrödinger hierarchy ⋮ An extension of the Kadomtsev-Petviashvili hierarchy and its Hamiltonian structures ⋮ Towards the construction of \(N=2\) supersymmetric integrable hierarchies ⋮ Central invariants of the constrained KP hierarchies ⋮ Bilinear equation and additional symmetries for an extension of the Kadomtsev-Petviashvili hierarchy ⋮ Rational reductions of the 2D-Toda hierarchy and mirror symmetry ⋮ Matrix formulation of Hamiltonian structures of constrained KP hierarchy ⋮ Exact correlators of two-matrix models ⋮ Hamiltonian Structures and Integrability of Frobenius Algebra-Valued (n, m)^th KdV Hierarchy ⋮ Toda lattice realization of integrable hierarchies ⋮ Dispersionful analog of the Whitham hierarchy ⋮ A Note on the Third Family of N = 2 Supersymmetric KdV Hierarchies

Cites Work

• What is a classical r-matrix?
• Lie algebras and equations of Korteweg-de Vries type
• Multi-field representations of the KP hierarchy and multi-matrix models
• An alternative approach to KP hierarchy in matrix models
• Intersection theory on the moduli space of curves and the matrix Airy function
• Constrained KP hierarchy and bi-Hamiltonian structures
• Exact solubility of Chern-Simons theory with compact simple gauge group
• Mathematics of dispersive water waves
• A FRACTIONAL KdV HIERARCHY
• Constraints of the Kadomtsev–Petviashvili hierarchy
• A simple model of the integrable Hamiltonian equation
• Nonperturbative two-dimensional quantum gravity

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