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We derive a fully discrete Inverse Scattering Transform as a method forsolving the initial-value problem for the Q3$_\delta$ lattice(difference-difference) equation for real-valued solutions. The initialcondition is given on an infinite staircase within an N-dimensional lattice andmust obey a given summability condition. The forward scattering problem isone-dimensional and the solution to Q3$_\delta$ is expressed through thesolution of a singular integral equation. The solutions obtained depend on Ndiscrete independent variables and N parameters.

A Discrete Inverse Scattering Transform for Q3$_\delta$