Description 
1 online resource (viii, 310 pages) : illustrations 
Contents 
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 sineGordon equation: its geometry and applications of current interest  4 Lobachevsky geometry and nonlinear equations of mathematical physics  5 NonEuclidean phase spaces. Discrete nets on the Lobachevsky plane and numerical integration algorithms for [Lambda]2equations  Bibliography  Index 
Summary 
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 sineGordon 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 nonEuclidean hyperbolic geometry 
Bibliography 
Includes bibliographical references and index 
Notes 
Translated from the Russian 

Online resource; title from PDF title page (SpringerLink, viewed August 15, 2014) 
Subject 
Geometry, Hyperbolic.

Form 
Electronic book

Author 
Iacob, A., translator

ISBN 
3319056689 (print) 

3319056697 (electronic bk.) 

9783319056685 (print) 

9783319056692 (electronic bk.) 
