半離散方程式の対称性と群不変解

彭, 林玉; 富田, 繁; 郡司, 士

doi:10.51094/jxiv.963

##article.authors##

彭, 林玉慶應義塾大学理工学部機械工学科 https://orcid.org/0000-0002-9255-8575 https://researchmap.jp/l.peng
富田, 繁慶應義塾大学理工学部機械工学科
郡司, 士慶應義塾大学理工学部機械工学科

DOI:

https://doi.org/10.51094/jxiv.963

キーワード:

半離散方程式、対称性、リー群、相似逓減、群不変解

抄録

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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