Discrete KdV and discrete modified KdV equations arising from motions of planar discrete curves (Q2883870)

The paper relates discrete differential geometry, with its notion of discrete curvature, and equicentroaffine discrete curvature, for piecewise linear planar curves, and two discrete integrable systems. The problem in discretizing an integrable system is the preservation of integrability. Previous connections between certain motions of planar curves and the modified KdV equation, respectively, are reviewed and exploited here to produce tangential motions on planar polygons which are related to the discrete KdV equations above.