General solutions to the Bäcklund transformation of Hirota's bilinear difference equation

Hirota's bilinear difference equation (discrete analogue of two dimensional Toda lattice) is formulated in a gauge symmetric form. A linear Backlund transformation is derived from the duality of gauge fields and field amplitudes and is solved explicitly. Some properties of the solutions and a relation to scattering amplitudes of the inverse scattering method are discussed.