208 citations · 1.4k across the 68 of their papers we have counts for
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Elliptic Solutions of ABS Lattice Equations
Frank W Nijhoff, James Atkinson
Elliptic N-soliton-type solutions, i.e. solutions emerging from the application of N consecutive Bäcklund transformations to an elliptic seed solution, are constructed for all equa…
A constructive approach to the soliton solutions of integrable quadrilateral lattice equations
James Atkinson, Frank Nijhoff
Scalar multidimensionally consistent quadrilateral lattice equations are studied. We explore a confluence between the superposition principle for solutions related by the Backlund…
Semi-classical Laguerre polynomials and a third order discrete integrable equation
P. E. Spicer, F. W. Nijhoff
A semi-discrete Lax pair formed from the differential system and recurrence relation for semi-classical orthogonal polynomials, leads to a discrete integrable equation for a specif…
Lagrangian multiforms and multidimensional consistency
Sarah Lobb, Frank Nijhoff
We show that well-chosen Lagrangians for a class of two-dimensional integrable lattice equations obey a closure relation when embedded in a higher dimensional lattice. On the basis…
Soliton Solutions for ABS Lattice Equations: I Cauchy Matrix Approach
Frank Nijhoff, James Atkinson, Jarmo Hietarinta
In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues o…