Multidimensional inverse scattering of integrable lattice equations

@article{Butler2012MultidimensionalIS,
  title={Multidimensional inverse scattering of integrable lattice equations},
  author={Samuel Butler},
  journal={Nonlinearity},
  year={2012},
  volume={25},
  pages={1613 - 1634}
}
We present a discrete inverse scattering transform for all ABS equations excluding Q4. The nonlinear partial difference equations presented in the ABS hierarchy represent a comprehensive class of scalar affine-linear lattice equations which possess the multidimensional consistency property. Due to this property it is natural to consider these equations living in an N-dimensional lattice, where the solutions depend on N distinct independent variables and associated parameters. The direct… 

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Inverse Scattering Transform Method for Lattice Equations

Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Mathematics and Statistics, Faculty of Science.

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