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Lobachevsky Geometry and Modern Nonlinear Problems / by Andrey Popov
版 | 1st ed. 2014. |
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出版者 | Cham : Springer International Publishing : Imprint: Birkhäuser |
出版年 | 2014 |
本文言語 | 英語 |
大きさ | VIII, 310 p. 103 illus : online resource |
著者標目 | *Popov, Andrey author SpringerLink (Online service) |
件 名 | LCSH:Algebraic geometry LCSH:Differential equations LCSH:Mathematical physics FREE:Algebraic Geometry FREE:Differential Equations FREE:Mathematical Physics |
一般注記 | Introduction -- 1 Foundations of Lobachevsky geometry: axiomatics, models, images in Euclidean space -- 2 The problem of realizing the Lobachevsky geometry in Euclidean space -- 3 The sine-Gordon equation: its geometry and applications of current interest -- 4 Lobachevsky geometry and nonlinear equations of mathematical physics -- 5 Non-Euclidean phase spaces. Discrete nets on the Lobachevsky plane and numerical integration algorithms for Λ2-equations -- Bibliography -- Index This monograph presents the basic concepts of hyperbolic Lobachevsky geometry and their possible applications to modern nonlinear applied problems in mathematics and physics, summarizing the findings of roughly the last hundred years. The central sections cover the classical building blocks of hyperbolic Lobachevsky geometry, pseudo spherical surfaces theory, net geometrical investigative techniques of nonlinear differential equations in partial derivatives, and their applications to the analysis of the physical models. As the sine-Gordon equation appears to have profound “geometrical roots” and numerous applications to modern nonlinear problems, it is treated as a universal “object” of investigation, connecting many of the problems discussed. The aim of this book is to form a general geometrical view on the different problems of modern mathematics, physics and natural science in general in the context of non-Euclidean hyperbolic geometry HTTP:URL=https://doi.org/10.1007/978-3-319-05669-2 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783319056692 |
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EB00233639 |
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※2017年9月4日以降