Dispersionless hierarchies, Hamilton-Jacobi theory and twistor correspondences

DOI10.1016/S0393-0440(97)00034-XzbMath0930.35165arXivsolv-int/9705013OpenAlexW3105670749WikidataQ126570402 ScholiaQ126570402MaRDI QIDQ1299141

Kanehisa Takasaki, Partha Guha

Publication date: 19 October 1999

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9705013

zbMATH Keywords

Riemann-Hilbert problemHamilton-Jacobi theorytwistor theoryKP and Toda hierarchies

Mathematics Subject Classification ID

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism (83C60)

Related Items

BIDIFFERENTIAL CALCULI, BICOMPLEX STRUCTURE AND ITS APPLICATION TO BIHAMILTONIAN SYSTEMS, The generalized Moyal–Nahm and continuous Moyal–Toda equations, On the dispersionless Davey–Stewartson hierarchy: Zakharov–Shabat equations, twistor structure, and Lax–Sato formalism, \(c\)-Map as \(c=1\) string, Einstein-Weyl geometry, the dKP equation and twistor theory

Cites Work

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• Quasi-classical limit of Toda hierarchy and \(W\)-infinity symmetries
• On the Benney equations
• SDiff(2) Toda equation --- hierarchy, tau function, and symmetries
• The dispersionless Lax equations and topological minimal models
• Hamiltonian formalism of Whitham-type hierarchies and topological Landau- Ginsburg models
• Nonlinear gravitons and curved twistor theory
• Integrable hierarchy underlying topological Landau-Ginzburg models of \(D\)-type
• Remarks on dispersionless KP, KdV, and 2D gravity
• Additional symmetries for integrable equations and conformal algebra representation
• An infinite hierarchy of conservation laws and nonlinear superposition principles for self-dual Einstein spaces
• Minitwistor spaces and Einstein-Weyl spaces
• Einstein-Weyl spaces and SU(∞) Toda fields
• SDIFF(2) KP HIERARCHY
• The τ‐function of the universal whitham hierarchy, matrix models and topological field theories
• INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT
• Symmetries of hyper-Kähler (or Poisson gauge field) hierarchy