TY - JOUR

T1 - A Constructive Approach to the Soliton Solutions of Integrable Quadrilateral Lattice Equations

AU - Atkinson, James

AU - Nijhoff, Frank

PY - 2010

Y1 - 2010

N2 - 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).

AB - 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).

U2 - 10.1007/s00220-010-1076-x

DO - 10.1007/s00220-010-1076-x

M3 - Article

VL - 299

SP - 283

EP - 304

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -