A Discrete Inverse Scattering Transform for Q3$_\delta$
Exactly Solvable and Integrable Systems
2012-10-09 v1
Abstract
We derive a fully discrete Inverse Scattering Transform as a method for solving the initial-value problem for the Q3 lattice (difference-difference) equation for real-valued solutions. The initial condition is given on an infinite staircase within an N-dimensional lattice and must obey a given summability condition. The forward scattering problem is one-dimensional and the solution to Q3 is expressed through the solution of a singular integral equation. The solutions obtained depend on N discrete independent variables and N parameters.
Cite
@article{arxiv.1210.1869,
title = {A Discrete Inverse Scattering Transform for Q3$_\delta$},
author = {Samuel Butler},
journal= {arXiv preprint arXiv:1210.1869},
year = {2012}
}
Comments
26 pages