Differential equations for Riemann and Prym theta-functions (Q1356300)

The note describes an infinite number of independent differential equations which can be associated to a compact Riemann surface as well as a double covering of compact Riemann surfaces ramified over 2 points. The systems include the KP-equation for a Riemann surface and the Veselov-Novikov equations for a Prym variety as special cases. For proofs and more details the author refers to the papers by B. A. Dubrovin and himself [see \textit{B. A. Dubrovin} and \textit{S. M. Natanzon}, Math. USSR, Izv. 32, No. 2, 269-288 (1989); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 52, No. 2, 267-286 (1988; Zbl 0672.35072)] and by himself [see \textit{S. M. Natanzon}, Funct. Anal. Appl. 26, No. 1, 13-20 (1992); translation from Funkts. Anal. Prilozh. 26, No. 1, 17-26 (1992; Zbl 0806.35022)].