2022 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 | Formal Lagrangian / Variational integrator / KdV equation / Symmetry reduction / Group-invariant solution / Similarity solution / Soliton / Variational principle |
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| Outline of Annual Research Achievements |
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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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
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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| Strategy for Future Research Activity |
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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| Causes of Carryover |
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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Research Products
(21 results)
