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Periodic discrete Darboux transforms
journal contributionposted on 2023-11-20, 16:50 authored by J Cho, K Leschke, Y Ogata
We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisation of the monodromy of the transformation. We also consider the integrable reduction to the case of discrete bicycle correspondence. Applying our method to the case of discrete circles, we obtain closed-form discrete parametrisations of all (closed) Darboux transforms and (closed) bicycle correspondences.
Leverhulme Trust Network Grant IN-2016-019
JSPS Research Fellowships for Young Scientist 21K13799
Author affiliationSchool of Computing and Mathematical Sciences, University of Leicester
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