Discrete mKdV and discrete sine-Gordon flows on discrete space curves

作者：Inoguchi Jun ichi^*; Kajiwara Kenji; Matsuura Nozomu; Ohta Yasuhiro

来源：Journal of Physics A-Mathematical and Theoretical, 2014, 47(23): 235202.

DOI：10.1088/1751-8113/47/23/235202

• discrete curve
• discrete integrable systems
• discrete mKdV equation
• discrete sine-Gordon equation

In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym-Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces.

• 出版日期2014-6-13