Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

Jun Ichi Inoguchi; Kenji Kajiwara; Nozomu Matsuura; Yasuhiro Ohta

doi:10.1088/1751-8113/45/4/045206

Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

Jun Ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura, Yasuhiro Ohta

Division of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms of the function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation.

Original language	English
Article number	045206
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	45
Issue number	4
DOIs	https://doi.org/10.1088/1751-8113/45/4/045206
Publication status	Published - Feb 3 2012

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Statistics and Probability
Modelling and Simulation
Mathematical Physics
Physics and Astronomy(all)

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10.1088/1751-8113/45/4/045206

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AB - We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms of the function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation.

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Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

Abstract

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