Symmetries and Group-Invariant Solutions of Semi-Discrete Equations
##article.authors##
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Linyu Peng
Department of Mechanical Engineering, Keio University
https://orcid.org/0000-0002-9255-8575
https://researchmap.jp/l.peng
- Shigeru Tomita Department of Mechanical Engineering, Keio University
- Mamoru Gunji Department of Mechanical Engineering, Keio University
DOI:
https://doi.org/10.51094/jxiv.963Keywords:
Semi-Discrete Equations, Symmetries, Lie Groups, Similarity Reduction, Group- Invariant SolutionsAbstract
半離散方程式（微分差分方程式ともいう）においては，連続独立変数と離散独立変数が非可換のため，対称性とならない非内在（non-intrinsic）（または不規則（irregular））な変換が生じるという問題があった．本論文では，この問題の解決方法を論じるとともに，半離散方程式における対称性理論について紹介する．具体例として，戸田型，ヴォルテラ型，5 点の伊藤・成田・ボゴヤヴレンスキー方程式などのリー点対称性（Lie point symmetry）を求め，群不変解（group-invariant solution）を導出する．
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Linyu Peng
Shigeru Tomita
Mamoru Gunji
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