A simple example of modular forms as tau-functions for integrable equations

zbMath0794.35114MaRDI QIDQ1311520

L. A. Takhtadzhyan

Publication date: 3 March 1994

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

group representationsmodular formsmoduli spacesself-dual Yang-Mills equationsintegrable equations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) PDEs in connection with quantum mechanics (35Q40) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Algebraic moduli problems, moduli of vector bundles (14D20) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Holomorphic modular forms of integral weight (11F11)

Related Items (13)

Gravity duals of \( \mathcal{N} \) = 2 SCFTs and asymptotic emergence of the electrostatic description ⋮ Second-order integrable Lagrangians and WDVV equations ⋮ Symbolic dynamics, modular curves, and Bianchi IX cosmologies ⋮ Geometric flows in Hořava-Lifshitz gravity gravity ⋮ Gravity, strings, modular and quasimodular forms ⋮ Triangle groups: automorphic forms and nonlinear differential equations ⋮ Nonintegrabilty of a Halphen system ⋮ AUTOMORPHISM OF SOLUTIONS TO RAMANUJAN'S DIFFERENTIAL EQUATIONS AND OTHER RESULTS ⋮ Transvectants, modular forms, and the Heisenberg algebra. ⋮ Integrable Lagrangians and modular forms ⋮ Analytic first integrals of the Halphen system ⋮ Aspects of Hecke symmetry: anomalies, curves, and chazy equations ⋮ Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model

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