Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Darboux dressing and undressing for the ultradiscrete KdV equation   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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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th