Lobachevsky Geometry and Modern Nonlinear Problems

  • Andrey Popov

About this book

Introduction

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.

Keywords

Tchebychev nets hyperbolic geometry nonlinear equations of mathematical physics pseudospherical surfaces sine-Gordon equation

Authors and affiliations

  • Andrey Popov
    • 1
  1. 1.Department of MathematicsLomonosov Moscow State UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-05669-2
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-05668-5
  • Online ISBN 978-3-319-05669-2
  • About this book