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Exact Solutions of Ultradiscrete Integrable Systems
https://doi.org/10.15083/00004020
https://doi.org/10.15083/00004020b851ac35-1c77-467f-acb2-6a0749ccd5cd
| 名前 / ファイル | ライセンス | アクション |
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IwaoS_22_3_PhD_a.pdf (4.8 MB)
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IwaoS_22_3_PhD_b.pdf (32.1 kB)
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| Item type | 学位論文 / Thesis or Dissertation(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2012-10-23 | |||||
| タイトル | ||||||
| タイトル | Exact Solutions of Ultradiscrete Integrable Systems | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_46ec | |||||
| タイプ | thesis | |||||
| ID登録 | ||||||
| ID登録 | 10.15083/00004020 | |||||
| ID登録タイプ | JaLC | |||||
| その他のタイトル | ||||||
| その他のタイトル | 超離散可積分系の厳密解 | |||||
| 著者 |
IWAO, Shinsuke
× IWAO, Shinsuke |
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| 著者別名 | ||||||
| 識別子Scheme | WEKO | |||||
| 識別子 | 9303 | |||||
| 姓名 | 岩尾, 慎介 | |||||
| 著者所属 | ||||||
| 著者所属 | 東京大学大学院数理科学研究科 | |||||
| 著者所属 | ||||||
| 著者所属 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| Abstract | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | The initial value problem of periodic box-ball systems is solved.Through a limiting procedure called ultradiscretisation, the box-ball system is obtainedfrom a reduced discrete KP equation. Our main theme is ultradiscretising the inverse scatteringmethod for discrete KP.Two key theorems in this thesis are listed below:a) The calculating method for the ultradiscrete limit of Abelian integrals over Riemanniansurfaces is established. A graphical method concerning tropical geometry is the essential toolfor the calculation.b) The explicit expression for the general solution of the reduced KP equation is obtained.The method bases on the inverse sacattering method. It is important to say that our methoddoes not depend on the Fay identity, or on any transcendental equations. In other words,our solutions are constructible.The conbination of these results allows us to analyse the periodic box-ball systems. Ourstrategy to solve the initial value problem is summerised as follows: (i) Lift the initial valueof the BBSs to the initial value of the KP equation. (ii) Solve the initial value problem of theKP equation (Key theorem b). The general solution is given as the combination of Riemanntheta functions. (iii) Ultradiscretise the solution of KP (Key theorem a). | |||||
| 書誌情報 | 発行日 2010-03-24 | |||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 410 | |||||
| 学位名 | ||||||
| 学位名 | 博士(数理科学) | |||||
| 学位 | ||||||
| 値 | doctoral | |||||
| 学位分野 | ||||||
| Mathematical Sciences (数理科学) | ||||||
| 学位授与機関 | ||||||
| 学位授与機関名 | University of Tokyo (東京大学) | |||||
| 研究科・専攻 | ||||||
| Graduate School of Mathematical Sciences (数理科学研究科) | ||||||
| 学位授与年月日 | ||||||
| 学位授与年月日 | 2010-03-24 | |||||
| 学位授与番号 | ||||||
| 学位授与番号 | 甲第26106号 | |||||
| 学位記番号 | ||||||
| 博数理第348号 | ||||||
