2002 Fiscal Year Final Research Report Summary
Development of the integrable equations and its application to engineering
| Project/Area Number |
13640407
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物理学一般
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| Research Institution | Nihon University |
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Principal Investigator |
KONNO Kimiaki Nihon University, College of Science and Technology, Professor, 理工学部, 教授 (50059606)
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| Co-Investigator(Kenkyū-buntansha) |
KAKUHATA Hiroshi Toyama University, College of Technology, Lecturer, 工学部, 講師 (50249174)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Nonlinear equation / integrable / IKK system / soliton / hierarchy / loop soliton / string / stretch |
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| Research Abstract |
The results of this project are summarized as the following four points.
1. We have found grand hierarchies for the systems of IKK scheme and the scheme with the modified Korteveg-de Vries hierarchy and the sine-Gordon hierarchy. We also found new integrable equations for the grand hierarchy of the IKK scheme.
2. We have obtained two kinds of loop soliton solutions for the IKK scheme. These are classified by the angular momentum of loop soliton. Interaction between solitons is investigated in detail.
3. We have discussed stability of the soliton for such a stand point of view as the stretching and shrinking of the loop soliton. One of the two nonlinear forces gives an effect of stretching of the loop and the other contributes shrinking of the loop. It is found that by balancing between stretching and shrinking forces for the loop stable loop soliton propagates along string.
4. We have numerically calculated initial value problem of the integrable vortex equation. We have found that the freezing of places where the stretching or shrinking of the vortex takes place. And we have also found pining of some initial vortex profiles.
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