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)

Access to Document

10.1142/S0219887819501007

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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.",

keywords = "Minkowski plane, defocusing mKdV equation, integrable systems, plane curves, solitons",

author = "Hyeongki Park and Inoguchi, {Jun Ichi} and Kenji Kajiwara and Maruno, {Ken Ichi} and Nozomu Matsuura and Yasuhiro Ohta",

note = "Funding Information: This work has been partially supported by JSPS KAKENHI Grant Numbers JP16H03941, JP18H01130, JP17H06127, JP15K04834, JP18K03435, JP15K04909, JP16K13763 and JP15K04862, and by JST CREST Grant Number JPMJCR14D4. One of the authors (H. P) acknowledges the support from the “Leading Program in Mathematics for Key Technologies” of Kyushu University.",

year = "2019",

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doi = "10.1142/S0219887819501007",

language = "English",

volume = "16",

journal = "International Journal of Geometric Methods in Modern Physics",

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T1 - Isoperimetric deformations of curves on the Minkowski plane

AU - Park, Hyeongki

AU - Inoguchi, Jun Ichi

AU - Kajiwara, Kenji

AU - Maruno, Ken Ichi

AU - Matsuura, Nozomu

AU - Ohta, Yasuhiro

N1 - Funding Information: This work has been partially supported by JSPS KAKENHI Grant Numbers JP16H03941, JP18H01130, JP17H06127, JP15K04834, JP18K03435, JP15K04909, JP16K13763 and JP15K04862, and by JST CREST Grant Number JPMJCR14D4. One of the authors (H. P) acknowledges the support from the “Leading Program in Mathematics for Key Technologies” of Kyushu University.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

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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