TY - BOOK ID - 700312 TI - Lobachevsky geometry and modern nonlinear problems AU - Popov, Andrey. AU - Iacob, A. PY - 2014 SN - 3319056697 3319056689 132213460X PB - Cham : Springer International Publishing : Imprint: Birkhäuser, DB - UniCat KW - Geometry, Hyperbolic. KW - Geometry, Algebraic. KW - Differential equations, Partial. KW - Partial differential equations KW - Algebraic geometry KW - Geometry KW - Hyperbolic geometry KW - Lobachevski geometry KW - Lobatschevski geometry KW - Geometry, Non-Euclidean KW - Geometry, algebraic. KW - Differential equations, partial. KW - Algebraic Geometry. KW - Partial Differential Equations. KW - Mathematical Physics. KW - Algebraic geometry. KW - Partial differential equations. KW - Mathematical physics. KW - Physical mathematics KW - Physics KW - Mathematics UR - https://www.unicat.be/uniCat?func=search&query=sysid:700312 AB - 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. ER -