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arXiv · 1903.07315

Darboux dressing and undressing for the ultradiscrete KdV equation

Jonathan J. C. Nimmo·Claire R. Gilson·R. Willox
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Abstract

We solve the direct scattering problem for the ultradiscrete Korteweg de Vries (udKdV) equation, over $\mathbb R$ for any potential with compact (finite) support, by explicitly constructing bound state and non-bound state eigenfunctions. We then show how to reconstruct the potential in the scattering problem at any time, using an ultradiscrete analogue of a Darboux transformation. This is achieved by obtaining data uniquely characterising the soliton content and the `background' from the initial potential by Darboux transformation.

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Jonathan J. C. Nimmo, Claire R. Gilson, R. Willox. 2019-03-18. Darboux dressing and undressing for the ultradiscrete KdV equation. https://doi.org/10.1088/1751-8121%2Fab45cf

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