Associativity equations in dispersionless integrable hierarchies

DOI10.1016/S0370-2693(01)00893-0zbMath0971.37031arXivhep-th/0105260OpenAlexW3100381470WikidataQ57587602 ScholiaQ57587602MaRDI QIDQ5941703

Andrei Marshakov, Oleg Ruchayskiy, Alexey Boyarsky, Anton V. Zabrodin, Paul B. Wiegmann

Publication date: 21 August 2001

Published in: Physics Letters. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/0105260

zbMATH Keywords

KP hierarchiesHirota equationsToda hierarchies

Mathematics Subject Classification ID

Related Items (28)

Time-dependent backgrounds of 2D string theory ⋮ String equations in Whitham hierarchies: τ-functions and Virasoro constraints ⋮ On kernel formulas and dispersionless Hirota equations of the extended dispersionless BKP hierarchy ⋮ On the solutions to the Witten-Dijkgraaf-Verlinde-Verlinde associativity equations and their algebraic properties ⋮ Hydrodynamic reductions of multidimensional dispersionless PDEs: The test for integrability ⋮ WDVV equation and triple-product relation ⋮ Remarks on the Waterbag Model of Dispersionless Toda Hierarchy ⋮ Infinite-dimensional Frobenius manifolds for \(2+1\) integrable systems ⋮ 2D string theory as normal matrix model ⋮ Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation ⋮ Exact solutions of integrable 2D contour dynamics ⋮ Duality transformations for generalized WDVV in Seiberg-Witten theory ⋮ Infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy ⋮ Recursion operator for a system with non-rational Lax representation ⋮ About the solutions to the Witten–Dijkgraaf– Verlinde–Verlinde associativity equations and their Lie-algebraic and geometric properties ⋮ Growth processes related to the dispersionless Lax equations ⋮ Universal Whitham hierarchy, dispersionless Hirota equations and multicomponent KP hierarchy ⋮ WDVV equations for 6d Seiberg-Witten theory and bi-elliptic curves ⋮ Coisotropic deformations of associative algebras and dispersionless integrable hierarchies ⋮ Integrability properties of Hurwitz partition functions. II. Multiplication of cut-and-join operators and WDVV equations ⋮ Kernel formula approach to the universal Whitham hierarchy ⋮ String equation for string theory on a circle ⋮ DV and WDVV ⋮ Matrix models, complex geometry, and integrable systems. II ⋮ Conformal mappings and dispersionless Toda hierarchy ⋮ FAY-LIKE IDENTITIES OF THE TODA LATTICE HIERARCHY AND ITS DISPERSIONLESS LIMIT ⋮ A note on reductions of the dispersionless Toda hierarchy ⋮ WDVV equations as functional relations

Cites Work

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• The τ‐function of the universal whitham hierarchy, matrix models and topological field theories
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