2015 Fiscal Year Final Research Report
Development of the approximation method based on the symmetry of systems
| Project/Area Number |
26800208
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Aichi Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2016-03-31
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| Keywords | 非線形動力学 / 数理物理学 / 漸近解析 / くりこみ群 |
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| Outline of Final Research Achievements |
Approximation methods are required when a differential equation is difficult to be exactly solved. In this study, a new approximation method is developed for partial differential equations in terms of the symmetry of the system. This method specifically works when we analyze perturbation problems. When we try to apply conventional method of this type developed before to partial differential equations, due to the increase of the independent variables, the system often has no symmetry necessary for the derivation of approximate solutions. However, it is found in this study that, by fixing a non-perturbation solution, construct constraint equations from it and consider this constraint equations as well as the original system, we can find symmetries which can be used to derive approximate solutions of the system.
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| Free Research Field |
非線形動力学
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