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 | |
| Publication status | Published - 2019 Jan 1 |
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Keywords
- defocusing mKdV equation
- integrable systems
- Minkowski plane
- plane curves
- solitons
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)
Cite this
Isoperimetric deformations of curves on the Minkowski plane. / Park, Hyeongki; Inoguchi, Jun Ichi; Kajiwara, Kenji; Maruno, Kenichi; Matsuura, Nozomu; Ohta, Yasuhiro.
In: International Journal of Geometric Methods in Modern Physics, 01.01.2019.Research output: Contribution to journal › Article
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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 -