Integrable hierarchy underlying topological Landau-Ginzburg models of D-type

Abstract

A universal integrable hierarchy underlying topological Landau-Ginzburg models of D-tye is presented. Like the dispersionless Toda hierarchy, the new hierarchy has two distinct (``positive" and ``negative") set of flows. Special solutions corresponding to topological Landau-Ginzburg models of D-type are characterized by a Riemann-Hilbert problem, which can be converted into a generalized hodograph transformation. This construction gives an embedding of the finite dimensional small phase space of these models into the full space of flows of this hierarchy. One of flat coordinates in the small phase space turns out to be identical to the first ``negative" time variable of the hierarchy, whereas the others belong to the ``positive" flows.

14 pages, Kyoto University KUCP-0061/93

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Cited by in corpus (12)

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• Dispersionless Toda hierarchy and two-dimensional string theory
• From Additional Symmetries to Linearization of Virasoro Symmetries
• On Kernel Formulas and Dispersionless Hirota Equations
• Block (or Hamiltonian) Lie symmetry of dispersionless D type Drinfeld-Sokolov hierarchy
• Topological Strings with Scaling Violation and Toda Lattice Hierarchy
• Bihamiltonian Structure of the Two-component Kadomtsev-Petviashvili Hierarchy of type B
• Generalized Drinfeld-Sokolov Hierarchies, Quantum Rings, and W-Gravity
• Dispersionless Hierarchies, Hamilton-Jacobi Theory and Twistor Correspondences
• $R$-matrices and Hamiltonian Structures for Certain Lax Equations
• A Class of Infinite-dimensional Frobenius Manifolds and Their Submanifolds
• Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality