Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves

摘要

We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the WadatiKonnoIchikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sineGordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the EulerLagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations.