Integrable systems and modular forms of level 2

Ablowitz, Mark J; Chakravarty, Sarbarsh; Hahn, Heekyoung

Integrable systems and modular forms of level 2

Authors

Ablowitz, Mark J

Chakravarty, Sarbarsh

Hahn, Heekyoung

Description

A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup $Γ_0(2)$ of the modular group $SL_2(\mathbb{Z})$ is constructed. These nonlinear equations are analogues of the well known Ramanujan equations, as well as the Chazy and Darboux-Halphen equations associated with the modular group. The general solutions of these equations can be realized in terms of the Schwarz trianle function $S(0,0,1/2; z)$.
PACS numbers: 02.30.Ik, 02.30.Hq, 02.10.De, 02.30.Gp