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Scalar multidimensionally consistent quadrilateral lattice equations arestudied. We explore a confluence between the superposition principle forsolutions related by the Backlund transformation, and the method of solving aRiccati map by exploiting two kn own particular solutions. This leads to anexpression for the N-soliton-type solutions of a generic equation within thisclass. As a particular instance we give an explicit N-soliton solution for theprimary model, which is Adler's lattice equation (or Q4).

A constructive approach to the soliton solutions of integrable quadrilateral lattice equations