| 研究課題/領域番号 |
20K14365
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| 研究機関 | 慶應義塾大学 |
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研究代表者 |
彭 林玉 慶應義塾大学, 理工学部(矢上), 講師 (90725780)
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| 研究期間 (年度) |
2020-04-01 – 2024-03-31
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| キーワード | Formal Lagrangian / Variational integrator / KdV equation / Symmetry reduction / Group-invariant solution / Similarity solution / Soliton / Variational principle |
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| 研究実績の概要 |
We proposed the modified formal Lagrangian structure for arbitrary differential equations and applied it to the derivation of conservation laws using Noether’s theorem. This is also used to constructing (formal) variational integrator for nonvariational equations. We also analyzed novel wave structures of a variable-coefficient KdV system by Hirota’s bilinear method and symmetry analysis; a variety of solitons were obtained as well as novel third-order Painleve equations.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
1: 当初の計画以上に進展している
理由
As planned, we have developed Noether’s theorems for discrete equations and have proposed structure-preserving numerical methods for non-variational differential equations based on the modified formal Lagrangian formulation. Several papers were published in leading academic journals together with a couple of invited international and domestic conference/workshop presentations.
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| 今後の研究の推進方策 |
The research will be continued following the original proposal. We have been studying the emerging of geometric integrator with machine learning as well.
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| 次年度使用額が生じた理由 |
Many conferences and workshops the principal investigator attended were held online in FY2022, and hence part of the budget is left for FY2023. This amount is going to be used to support the organization of an international workshop related to the current research project in FY2023, which was not planned during the application stage. The principal investigator is one of the organizers.
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