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
SN - 0010-3616
VL - 299
SP - 283
EP - 304
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -