Lobachevsky Geometry and Modern Nonlinear Problems

Portada
Springer, 6 d’ag. 2014 - 310 pàgines

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.

 

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Continguts

Introduction
1
axiomatics models images in Euclidean space
15
Chapter 2 The problem of realizing the Lobachevsky geometry in Euclidean space
61
its geometry and applications of current interest
127
Chapter 4 Lobachevsky geometry and nonlinear equations of mathematical physics
225
Chapter 5 NonEuclidean phase spaces Discrete nets on the Lobachevsky plane and numerical integration algorithms for Λ2equations
259
Bibliography
291
Index
307
Copyright

Altres edicions - Mostra-ho tot

Lobachevsky Geometry and Modern Nonlinear Problems
Andrey Popov
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Lobachevsky Geometry and Modern Nonlinear Problems
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Lobachevsky Geometry and Modern Nonlinear Problems
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Previsualització no disponible - 2014

Frases i termes més freqüents

absolute algorithm Amsler surface angle asymptotic lines Axiom of Parallels Bäcklund transformation Cauchy problem Chebyshev Chebyshev equation circles classical coefficients condition connected considered const constant negative curvature construction coordinate lines corresponding curve cuspidal edges Darboux problem defined denote derivatives disc domain equidistant Euclidean space Euclidean space E3 expression Figure formula functions G-equation Gauss Gaussian curvature geodesic curvature given half-plane horocycles hyperbolic geometry integration irregular edges isometric immersion Korteweg-de Vries equation linear Lobachevsky geometry Lobachevsky plane manifold mathematical physics method non-Euclidean geometry nonlinear equations obtained one-soliton solution orthogonal Painlevé parameter partial differential equations phase trajectory Poincaré point at infinity pseudospherical metric pseudospherical surface radius vector realization relations result right-hand side second fundamental form segment sine-Gordon equation soliton solution z(t straight line Subsection system of equations tangent Theorem theory tion two-dimensional two-soliton values variables

Informació bibliogràfica

TítolLobachevsky Geometry and Modern Nonlinear Problems
AutorAndrey Popov
Traducció deAndrei Iacob
Edicióil·lustrada
EditorSpringer, 2014
ISBN3319056697, 9783319056692
Nre. de pàgines310 pàgines
  
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