@article {IOPORT.05586493,
    author       = {Inoue, Rei and Takenawa, Tomoyuki},
    title        = {A tropical analogue of Fay's trisecant identity and the ultra-discrete periodic Toda lattice.},
    year         = {2009},
    journal      = {Communications in Mathematical Physics},
    volume       = {289},
    number       = {3},
    issn         = {0010-3616},
    pages        = {995-1021},
    publisher    = {Springer-Verlag, Berlin},
    doi          = {10.1007/s00220-009-0815-3},
    abstract     = {Fay's trisecant identity for Riemann's theta function, associated with an algebraic curve, was established in [{\it J. D. Fay}, Theta functions on Riemann surfaces. Lecture Notes in Mathematics. 352. Berlin-Heidelberg-New York: Springer-Verlag (1973; Zbl 0281.30013)]. In the paper under review, the tropical version of this identity is established for certain special hyperelliptic tropical curves (and conjectured for an arbitrary tropical curve). In particular, the ultra-discrete periodic Toda lattice system $T$ can be transformed into a special case of Fay's trisecant identity for a tropical spectral curve of $T$, which allows the authors to obtain the general solution of $T$ in terms of the corresponding tropical Riemann's theta function.},
    reviewer     = {Alexander Esterov (Moscow)},
    identifier   = {05586493},
}