Remarks on dispersionless KP, KdV, and 2D gravity

DOI10.1007/BF02430644zbMath0814.35117OpenAlexW1998322978MaRDI QIDQ1341674

Robert W. Carroll

Publication date: 22 June 1995

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02430644

zbMATH Keywords

string equationinverse scattering dataaction angle variablesHirota bilinear formulasLandau-Ginsburg equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items

Integrability properties of the dispersionless Kadomtsev-Petviashvili hierarchy, The whitham equations revisited, On the Miura Map between the dispersionless KP and dispersionless modified KP hierarchies, Some survey remarks on Whitham theory and Em duality, Dispersionless hierarchies, Hamilton-Jacobi theory and twistor correspondences

Cites Work

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• Quasi-classical limit of Toda hierarchy and \(W\)-infinity symmetries
• Geometry of the string equations
• Geometric realization of conformal field theory on Riemann surfaces
• An alternative approach to KP hierarchy in matrix models
• SDiff(2) Toda equation --- hierarchy, tau function, and symmetries
• The dispersionless Lax equations and topological minimal models
• Toward a canonical formalism of non-perturbative two-dimensional gravity
• Hamiltonian formalism of Whitham-type hierarchies and topological Landau- Ginsburg models
• A matrix integral solution to two-dimensional \(W_ p\)-gravity
• The isomonodromy approach to matrix models in 2D quantum gravity
• Explicit solution for \(p\)--\(q\) duality in two-dimensional quantum gravity
• \(D\) bar dressing and Sato theory
• Integrable hierarchy underlying topological Landau-Ginzburg models of \(D\)-type
• Additional symmetries for integrable equations and conformal algebra representation
• On canonical coordinates in soliton hierarchies
• ADDITIONAL SYMMETRIES OF KP, GRASSMANNIAN, AND THE STRING EQUATION
• HIROTA BILINEAR FORM FOR THE SUPER-KdV HIERARCHY
• ACTION PRINCIPLE FOR STRINGS IN LESS THAN ONE DIMENSION
• Mastersymmetries, Higher Order Time-Dependent Symmetries and Conserved Densities of Nonlinear Evolution Equations
• THE LAX OPERATOR APPROACH FOR THE VIRASORO AND THE W-CONSTRAINTS IN THE GENERALIZED KdV HIERARCHY
• GEOMETRY OF UNIVERSAL GRASSMANN MANIFOLD FROM ALGEBRAIC POINT OF VIEW
• CATEGORY OF VECTOR BUNDLES ON ALGEBRAIC CURVES AND INFINITE DIMENSIONAL GRASSMANNIANS
• SOLITON EQUATIONS AND THE VIRASORO ALGEBRA
• Conserved quantities and symmetries of KP hierarchy
• A theorem about Hamiltonian systems
• Integrable Models
• SDIFF(2) KP HIERARCHY
• Some remarks on symmetries, dressing, and virasoro action
• The τ‐function of the universal whitham hierarchy, matrix models and topological field theories
• INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT
• Symmetries, sato theory, and tau functions