Isoperimetric deformations of curves on the Minkowski plane

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

doi:10.1142/S0219887819501007

Isoperimetric deformations of curves on the Minkowski plane

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

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article

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
Journal	International Journal of Geometric Methods in Modern Physics
DOIs	https://doi.org/10.1142/S0219887819501007
Publication status	Published - 2019 Jan 1

Keywords

defocusing mKdV equation
integrable systems
Minkowski plane
plane curves
solitons

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

Access to Document

10.1142/S0219887819501007

Fingerprint Dive into the research topics of 'Isoperimetric deformations of curves on the Minkowski plane'. Together they form a unique fingerprint.

Cite this

Park, H., Inoguchi, J. I., Kajiwara, K., Maruno, K., Matsuura, N., & Ohta, Y. (2019). Isoperimetric deformations of curves on the Minkowski plane. International Journal of Geometric Methods in Modern Physics. https://doi.org/10.1142/S0219887819501007

@article{571c0f8ea1ce4ccf8a2fd97080962bab,

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

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

year = "2019",

month = jan,

day = "1",

doi = "10.1142/S0219887819501007",

language = "English",

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

issn = "0219-8878",

publisher = "World Scientific Publishing Co. Pte Ltd",

}

TY - JOUR

T1 - Isoperimetric deformations of curves on the Minkowski plane

AU - Park, Hyeongki

AU - Inoguchi, Jun Ichi

AU - Kajiwara, Kenji

AU - Maruno, Kenichi

AU - Matsuura, Nozomu

AU - Ohta, Yasuhiro

PY - 2019/1/1

Y1 - 2019/1/1

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 - defocusing mKdV equation

KW - integrable systems

KW - Minkowski plane

KW - plane curves

KW - solitons

UR - http://www.scopus.com/inward/record.url?scp=85067123510&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067123510&partnerID=8YFLogxK

U2 - 10.1142/S0219887819501007

DO - 10.1142/S0219887819501007

M3 - Article

AN - SCOPUS:85067123510

JO - International Journal of Geometric Methods in Modern Physics

JF - International Journal of Geometric Methods in Modern Physics

SN - 0219-8878

ER -