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The generalised Backlund transformations connecting two different solutions of non-linear partial differential-difference equations solvable by an inverse method are determined. The scattering problem for the inverse method is the discretised scalar Schrodinger equation. In particular the Backlund transformations relating two different solutions of the same equation and a transformation between a solution of the same equation at two different times are presented.
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R. K. Dodd (1978) studied this question.
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