Isogonal Deformation of Discrete Plane Curves and Discrete Burgers Hierarchy

2015/11/13 by Kenji Kajiwara, Kajiwara, Kenji, Toshinobu Kuroda +3
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · doi:10.48550/arxiv.1511.04152

arxiv created 2016/03/13 · arxiv updated 2016/03/15

Abstract

We study deformations of plane curves in the similarity geometry. It is known that continuous deformations of smooth curves are described by the Burgers hierarchy. In this paper, we formulate the discrete deformation of discrete plane curves described by the discrete Burgers hierarchy as isogonal deformations. We also construct explicit formulas for the curve deformations by using the solution of linear diffusion differential/difference equations.

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