Lobachevsky Geometry and Modern Nonlinear Problems

• Main Author: Popov, Andrey (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2014.
• Subjects: Mathematics.; Algebraic geometry.; Partial differential equations.; Mathematical physics.; Algebraic Geometry.; Partial Differential Equations.; Mathematical Physics.

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 hyper...

Table of 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 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 Λ2-equations
• Bibliography
• Index.