Isoperimetric deformations of curves on the Minkowski plane

Hyeongki Park; Jun Ichi Inoguchi; Kenji Kajiwara; Ken Ichi Maruno; Nozomu Matsuura; Yasuhiro Ohta

doi:10.1142/S0219887819501007

Isoperimetric deformations of curves on the Minkowski plane

Hyeongki Park, Jun Ichi Inoguchi, Kenji Kajiwara, Ken Ichi Maruno, Nozomu Matsuura, Yasuhiro Ohta

School of Fundamental Science and Engineering

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

Abstract

We formulate an isoperimetric deformation of curves on the Minkowski plane, which is governed by the defocusing modified Korteweg-de Vries (mKdV) equation. Two classes of exact solutions to the defocusing mKdV equation are also presented in terms of the τ 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 gives regular solutions to the defocusing mKdV equation. Some pictures illustrating the typical dynamics of the curves are presented.

Original language	English
Article number	1950100
Journal	International Journal of Geometric Methods in Modern Physics
Volume	16
Issue number	7
DOIs	https://doi.org/10.1142/S0219887819501007
Publication status	Published - 2019 Jul 1

Keywords

Minkowski plane
defocusing mKdV equation
integrable systems
plane curves
solitons

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

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10.1142/S0219887819501007

Cite this

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title = "Isoperimetric deformations of curves on the Minkowski plane",

abstract = "We formulate an isoperimetric deformation of curves on the Minkowski plane, which is governed by the defocusing modified Korteweg-de Vries (mKdV) equation. Two classes of exact solutions to the defocusing mKdV equation are also presented in terms of the τ 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 gives regular solutions to the defocusing mKdV equation. Some pictures illustrating the typical dynamics of the curves are presented.",

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AU - Park, Hyeongki

AU - Inoguchi, Jun Ichi

AU - Kajiwara, Kenji

AU - Maruno, Ken Ichi

AU - Matsuura, Nozomu

AU - Ohta, Yasuhiro

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AB - We formulate an isoperimetric deformation of curves on the Minkowski plane, which is governed by the defocusing modified Korteweg-de Vries (mKdV) equation. Two classes of exact solutions to the defocusing mKdV equation are also presented in terms of the τ 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 gives regular solutions to the defocusing mKdV equation. Some pictures illustrating the typical dynamics of the curves are presented.

KW - Minkowski plane

KW - defocusing mKdV equation

KW - integrable systems

KW - plane curves

KW - solitons

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Isoperimetric deformations of curves on the Minkowski plane

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Keywords

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