A Constructive Approach to the Soliton Solutions of Integrable Quadrilateral Lattice Equations

Scalar multidimensionally consistent quadrilateral lattice equations are studied. We explore a confluence between the superposition principle for solutions related by the Bäcklund transformation, and the method of solving a Riccati map by exploiting two known particular solutions. This leads to an expression for the N-soliton-type solutions of a generic equation within this class. As a particular instance we give an explicit N-soliton solution for the primary model, which is Adler’s lattice equation (or Q4).