Non-Euclidean phase spaces. Discrete nets on the Lobachevsky plane and numerical integration algorithms for $$\Lambda^2$$ -equations

Andrey Popov
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Andrey Popov: Lomonosov Moscow State University, Department of Mathematics

Chapter Chapter 5 in Lobachevsky Geometry and Modern Nonlinear Problems, 2014, pp 259-290 from Springer

Abstract: Abstract In this chapter we apply the geometric Gaussian formalism for nonlinear equations of theoretical physics presented in Chapter 4 to the theory of difference methods for the numerical integration of differential equations. The first part of the chapter (§§ 5.1. and 5.2) is devoted to introducing the concept of non-Euclidean phase spaces, which are nonlinear analogs (with nontrivial curvature) of the phase spaces of classical mechanics, statistical physics, and of the Minkowski space of the special theory of relativity.

Keywords: Magnetization Vector; Invariant State; Phase Trajectory; Ultrashort Pulse; Observable Quantity (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-05669-2_6

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DOI: 10.1007/978-3-319-05669-2_6

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