  Tropical R is the birational map that intertwines products of geometric
crystals and satisfies the Yang-Baxter equation. We show that the D^{(1)}_n
tropical R introduced by the authors and its reduction to A^{(2)}_{2n-1} and
C^{(1)}_n are equivalent to a system of bilinear difference equations of Hirota
type. Associated tropical vertex models admit solutions in terms of tau
functions of the BKP and DKP hierarchies.
