Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves
Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves
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DOI：
10.1088/1751-8113/44/39/395201
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发表时间：
2011-07
期刊：
影响因子：
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通讯作者：
B. Feng;J. Inoguchi;K. Kajiwara;K. Maruno;Y. Ohta
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文献类型：
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作者：
B. Feng;J. Inoguchi;K. Kajiwara;K. Maruno;Y. Ohta
我们考虑了一些与平面曲线运动有关的孤子方程的可积离散：Wadati-Konno-Ichikawa弹性梁方程、复Dym方程和短脉冲方程。它们通过速度图变换与修正的KdV方程或Sine-Gordon方程相联系。基于速度图变换被看作是曲线运动的欧拉-拉格朗日变换的观察，我们构造了速度图变换的离散类似物，从而得到了这些孤子方程的可积离散。
We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati–Konno–Ichikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sine–Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler–Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations.