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

The authors show how classical modular forms and functions appear a tau-functions for a certain integrable reduction of the self-dual-Yang-Mills equations obtained by S. Chakravarty, M. Ablowitz, and P. Clarkson. The possible consequences are discussed of this novel phenomenon in integrable systems which indicate deep connections between integrable equations, group representations, modular forms, and moduli spaces. 27 refs