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.
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Project (external):
Leverhulme Trust Japan Society for the Promotion of Science
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Project ID:
IN-2016-019 21K13799
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Research Areas:
Logic and Computation: 5% Mathematical and Algorithmic Foundations: 5% Fundamental Mathematics Research: 90%
