Isoperimetric deformations of curves on the Minkowski plane
Differential Geometry
2019-09-04 v1 Exactly Solvable and Integrable Systems
Abstract
We formulate an isoperimetric deformation of curves on the Minkowski plane, which is governed by the defocusing mKdV equation. Two classes of exact solutions to the defocusing mKdV equation are also presented in terms of the functions. By using one of these classes, we construct an explicit formula for the corresponding motion of curves on the Minkowski plane even though those solutions have singular points. Another class give regular solutions to the defocusing mKdV equation. Some pictures illustrating typical dynamics of the curves are presented.
Keywords
Cite
@article{arxiv.1807.07736,
title = {Isoperimetric deformations of curves on the Minkowski plane},
author = {Hyeongki Park and Jun-ichi Inoguchi and Kenji Kajiwara and Ken-ichi Maruno and Nozomu Matsuura and Yasuhiro Ohta},
journal= {arXiv preprint arXiv:1807.07736},
year = {2019}
}