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 |
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Article number | 045206 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 45 |
Issue number | 4 |
DOIs | |
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)