We discuss addition-theorems-type functional equations which naturally arise in various problems of mathematical physics and topology (Toda and Calogero-Moser dynamical systems, rational and pole solutions of the KdV equation; elliptic genera associated with the string-inspired Witten index).
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/158