2014 Fiscal Year Final Research Report
Study on one-dimensional elastic bodies with a focus on Kirchhoff elastic rods in space forms
| Project/Area Number |
23540116
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Fukuoka University |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Keywords | キルヒホッフ弾性棒 / 弾性曲線 / 変分問題 / 渦糸 / 局所誘導階層 / ソリトン曲線 / 変形KdV方程式 |
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| Outline of Final Research Achievements |
The initial-value problem for the equations of Kirchhoff elastic rods in complete Riemannian manifolds was studied, and it was proven that there exists a unique global solution of this initial-value problem. Also, a class of fourth soliton curves in three-dimensional Euclidean space was explicitly expressed in terms of Jacobi elliptic functions, and it was proven that there exist periodic solutions in this class. Each periodic solution winds around a torus of revolution. By using these periodic fourth soliton curves, congruence solutions (solutions moving without change of shape) of the "space curve version of the modified KdV equation" were constructed.
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| Free Research Field |
幾何学
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