# Soliton solutions for ABS lattice equations: I. Cauchy matrix approach

@article{Nijhoff2009SolitonSF, title={Soliton solutions for ABS lattice equations: I. Cauchy matrix approach}, author={Frank W Nijhoff and James Atkinson and Jarmo Hietarinta}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2009}, volume={42}, pages={404005} }

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 of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case, there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations ‘of KdV type’ that were known since the late 1970s and early 1980s. In this…

## 108 Citations

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In Part I soliton solutions to the ABS list of multi-dimensionally consistent difference equations (except Q4) were derived using connection between the Q3 equation and the NQC equations, and then by…

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