Lobachevsky geometry and modern nonlinear problems

著者

書誌事項

Lobachevsky geometry and modern nonlinear problems

Andrey Popov ; translated by Andrei Iacob

Birkhäuser , Springer, c2014

タイトル別名

Геометрия лобачевского и математическая физика

大学図書館所蔵 件 / 全9件

この図書・雑誌をさがす

注記

"Original Russian editon, Геометрия лобачевского и математическая физика (Lobachevsky geometry and mathematical physics) by Andrey Popov, published by the Publishing House of Physical Department of Lomonosov Moscow State University, Moscow, 2012, ISBN 9785827901044."--T.p. verso

Including bibliographical references (p. 291-305) and index

内容説明・目次

内容説明

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.

目次

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 2-equations.- Bibliography.- Index.

「Nielsen BookData」 より

詳細情報

ページトップへ