Integrable systems and modular forms of level 2

DOI10.1088/0305-4470/39/50/003zbMath1123.37031arXivmath/0609210OpenAlexW2963927206MaRDI QIDQ3418459

Sarbarish Chakravarty, Heekyoung Hahn, Mark J. Ablowitz

Publication date: 5 February 2007

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609210

zbMATH Keywords

Chazy equationsDarboux-Halphen equationsRamanujan equationsnonlinear differential equations associated with the Eisenstein series

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Holomorphic modular forms of integral weight (11F11) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (14)

Special solutions to Chazy equation ⋮ Nonlinear differential equations satisfied by certain classical modular forms ⋮ Linearizable Abel equations and the Gurevich–Pitaevskii problem ⋮ The sixth Painlevé transcendent and uniformization of algebraic curves ⋮ Triangle groups: automorphic forms and nonlinear differential equations ⋮ An approach to BPS black hole microstate counting in an \(N = 2\) STU model ⋮ SECOND-ORDER QUASILINEAR PDEs AND CONFORMAL STRUCTURES IN PROJECTIVE SPACE ⋮ Integrable Lagrangians and modular forms ⋮ Bianchi-IX, Darboux–Halphen and Chazy–Ramanujan ⋮ Note on Halphen's system ⋮ Parameterizations of the Chazy Equation ⋮ Differential equations involving cubic theta functions and Eisenstein series ⋮ Dynamical systems defining Jacobi's ϑ-constants ⋮ Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions

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