It is proposed that phase spaces of nonzero cunature (non-Euclidean phase spaces) be used to describe physical phenomena. The singularities of these spaces show good correspondence to the invariant (equilibrium) states of physical systems. Pseudospherical phase spaces are investigated for which the Lobachevski geometry is valid. General principles are stated for the evolution of phenomena described, in particular, by the sin-Gordon, Korteweg-de Vries, Burgers, Liouville, and other equations.
Department of Mathematics, Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia
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