TY - JOUR
T1 - Elliptic N-soliton Solutions of ABS Lattice Equations
AU - Nijhoff, Frank
AU - Atkinson, James
PY - 2010
Y1 - 2010
N2 - Elliptic N-soliton-type solutions, that is, solutions emerging from the application of N consecutive Bäcklund transformations to an elliptic seed solution, are constructed for all equations in the Adler-Bobenko-Suris (ABS) list of quadrilateral lattice equations, except for the case of the Q4 equation which is treated elsewhere. The main construction, which is based on an elliptic Cauchy matrix, is performed for the equation Q3, and by coalescence on certain auxiliary parameters, the corresponding solutions of the remaining equations in the list are obtained. Furthermore, the underlying linear structure of the equations is exhibited, leading, in particular, to a novel Lax representation of the Q3 equation.
AB - Elliptic N-soliton-type solutions, that is, solutions emerging from the application of N consecutive Bäcklund transformations to an elliptic seed solution, are constructed for all equations in the Adler-Bobenko-Suris (ABS) list of quadrilateral lattice equations, except for the case of the Q4 equation which is treated elsewhere. The main construction, which is based on an elliptic Cauchy matrix, is performed for the equation Q3, and by coalescence on certain auxiliary parameters, the corresponding solutions of the remaining equations in the list are obtained. Furthermore, the underlying linear structure of the equations is exhibited, leading, in particular, to a novel Lax representation of the Q3 equation.
UR - https://www.scopus.com/pages/publications/78149245252
U2 - 10.1093/imrn/rnq010
DO - 10.1093/imrn/rnq010
M3 - Article
SN - 1073-7928
VL - 2010
SP - 3837
EP - 3895
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 20
ER -