2020 Fiscal Year Research-status Report
Multisymplectic Geometry and Geometric Numerical Integrator for Variational Problems
| Project/Area Number |
20K14365
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| Research Institution | Keio University |
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Principal Investigator |
彭 林玉 慶應義塾大学, 理工学部(矢上), 講師 (90725780)
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | 修正形式ラグランジアン / ハミルトン偏微分方程式 |
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| Outline of Annual Research Achievements |
Purpose of this project is to understand symplectic and multisymplectic theories of arbitrary order variational differential equations. In the first year, the following results were achieved.
1. We reviewed the multisymplectic theories of first-order variational problems and revealed their connections with Hamiltonian PDEs.
2. We constructed a modified formal Lagrangian formulation that allows us, at least formally, to establish a variational principle for an arbitrary system of differential equations.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The research of the first stage planned in the proposal has been commenced. We were able to move a bit further by developing the modified formal Lagrangian formulation.
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| Strategy for Future Research Activity |
The research will be continued following the original proposal.
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| Causes of Carryover |
Due to COVID-19, many academic conferences of FY2020 were held online, and consequently travelling was not able to be commenced. Since we know the virus better now, I hope to pay some (at least domestic) academic visits in FY2021 under the premise of proper protection.
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