
Lobachevsky Geometry and Modern Nonlinear Problems
Andrey Popov(Author)
Springer (Publisher)
Published on 20. August 2014
Book
Hardback
VIII, 310 pages
978-3-319-05668-5 (ISBN)
Description
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.
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.
Reviews / Votes
"The main aim of this book is to look at the potential of the geometry developed by Lobachevskii in the context of its emergence in various branches of current interest in contemporary mathematics and science, especially in nonlinear problems of mathematical physics. ... the book is well written, very readable, and nicely illustrated throughout with many graphs and figures, especially figures of surfaces. ... This unique book makes this difficult subject interesting and within reach." (Paul F. Bracken, Mathematical Reviews, August, 2015) "The book is original in its form and content. It covers a wide spectrum of geometry and analysis and it displays the Lobachevsky plane as a central object in the study of the classical equations of mathematical physics. The style is expository and clear. This book is a valuable addition to the geometric literature." (Athanase Papadopoulos, zbMATH 1311.51002, 2015)More details
Product info
Book
Language
English
Place of publication
Cham
Switzerland
Target group
Research
Illustrations
103 s/w Abbildungen
103 schwarz-weiße Abbildungen, Bibliographie
Dimensions
Height: 244 mm
Width: 164 mm
Thickness: 22 mm
Weight
618 gr
ISBN-13
978-3-319-05668-5 (9783319056685)
DOI
10.1007/978-3-319-05669-2
Schweitzer Classification
Other editions
Additional editions

Andrey Popov
Lobachevsky Geometry and Modern Nonlinear Problems
Book
09/2016
Birkhäuser
€106.99
Shipment within 10-15 days

Andrey Popov
Lobachevsky Geometry and Modern Nonlinear Problems
E-Book
08/2014
1st Edition
Birkhäuser
€96.29
Available for download
Persons
Content
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.