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Symmetric Approach for Integrable Nonlinear Eolution Equations in 1-Space and 1-Time Dimensions
https://doi.org/10.15099/00004408
https://doi.org/10.15099/000044082bf1dbe5-e71f-4b87-be64-23d74fe28af2
名前 / ファイル | ライセンス | アクション |
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Kokiyo_41_01_Page050to068.pdf (1.2 MB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2012-10-10 | |||||
タイトル | ||||||
タイトル | Symmetric Approach for Integrable Nonlinear Eolution Equations in 1-Space and 1-Time Dimensions | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 時空(1+1)次元 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 1-Space and 1-Time Dimensions | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 非線型発展方式 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Nonlinear Eolution Equations | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | シンメトリック・アプローチ | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Symmetric Approach | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | GGKM | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | NLEE | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | ISM | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | KdV | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
ID登録 | ||||||
ID登録 | 10.15099/00004408 | |||||
ID登録タイプ | JaLC | |||||
著者 |
川田, 勉
× 川田, 勉 |
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著者別名 | ||||||
識別子Scheme | WEKO | |||||
識別子 | 57256 | |||||
姓名 | Kawata, Tsutomu | |||||
その他(別言語等)のタイトル | ||||||
その他のタイトル | 時空(1+1)次元における非線型発展方式のシンメトリック・アプローチ | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | Since the famous investigation of the KdV equation b y GGKM, both existence of infinitely many conservation laws and the hierarchy of nonlinear evolution equations (NLLEs) had been understood as essential for a given NLEE to be integrable. This problem was studied by many authors, but we remark the contribution by Magri, who had explained these properties from the view of geometrical point. Starting from symmetries (contravariant quantity), he introduced a potential operator (covariant quantity) and a sympletic operator which maps the covariant to the contravariant. The conseration laws were simply derived and he proposed a "bi-H amiltonian structure" for integrable systems. Fuchsteiner deeply considered symmetries and introduced both concepts of strong symmetries and hereditary symmetries. Fokas had used a Lie-Backlund transformation and also arrived at the hereditary symmetry. Their idear was further developed and connections with the Backlund transformation and with the cannonical structures were made clear. The iso-spectral problem is essential for the inverse spectral method (ISM) and its relation with the symmetric approach is very interesting. Such relations were first treated by Lax for the case of KdV equation and extended to other cases. The motiation of this issue is to detail with the review of the symmetric approach. We specially consider a certain linear integra-differential operator K_± and make clear the role of squared eigenfunctions which is closely related with the 2 X 2-matrix isospectral problem. We inspect that this operator is both strong and hereditary symmetries and make clear the associated cannonical structures. Considering that K_± are also obtained by the compatibility condition of NLLEs, we propose a direct and simple method for developing the hereditary symmetries with a N x N-matrix formula. |
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引用 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 富山大学工学部紀要,41 | |||||
書誌情報 |
富山大学工学部紀要 巻 41, p. 50-68, 発行日 1990-03 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 03871339 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AN00175872 | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
国立国会図書館分類 | ||||||
主題Scheme | NDLC | |||||
主題 | ZM2 | |||||
出版者 | ||||||
出版者 | 富山大学工学部 | |||||
資源タイプ(DSpace) | ||||||
内容記述タイプ | Other | |||||
内容記述 | Article |
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Cite as
川田, 勉, 1990, Symmetric Approach for Integrable Nonlinear Eolution Equations in 1-Space and 1-Time Dimensions: 富山大学工学部, 50–68 p.
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