String theories and Hirota's bilinear difference equation.

The ratio of an N-point p-loop string amplitude to the N-point tree amplitude is shown to solve Hirota's bilinear difference equation which is satisfied by all solutions to the Kadomtsev-Petviashvili hierarchy. Evolution of solutions is determined by Koba-Nielsen variables and external momenta. Fay's trisecant formula emerges as a result.