研究課題/領域番号 |
20K14365
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研究種目 |
若手研究
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配分区分 | 基金 |
審査区分 |
小区分12040:応用数学および統計数学関連
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研究機関 | 慶應義塾大学 |
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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研究課題ステータス |
交付 (2022年度)
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配分額 *注記 |
3,250千円 (直接経費: 2,500千円、間接経費: 750千円)
2023年度: 780千円 (直接経費: 600千円、間接経費: 180千円)
2022年度: 780千円 (直接経費: 600千円、間接経費: 180千円)
2021年度: 1,040千円 (直接経費: 800千円、間接経費: 240千円)
2020年度: 650千円 (直接経費: 500千円、間接経費: 150千円)
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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 / Noether's theorem / Symmetry / Conservation law / DPD / Hamiltonian system / 修正形式ラグランジアン / ハミルトン偏微分方程式 / Symplectic structure / Geometric integrator / Variational bicomplex / Variational problems / PDEs |
研究開始時の研究の概要 |
Geometric integrator is among one of the most efficient numerical methods for differential equations. In this project, we establish a unified and systematical analogue for understanding both continuous and discrete multisymplectic structures of arbitrary order variational differential equations.
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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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