TY - GEN digital ID - 131515549 TI - Lobachevsky Geometry and Modern Nonlinear Problems PY - 2014 SN - 9783319056692 PB - Cham Springer International Publishing, Imprint: Birkhäuser DB - UniCat KW - Mathematics KW - Algebraic geometry KW - Geometry KW - Partial differential equations KW - Differential equations KW - Mathematical physics KW - differentiaalvergelijkingen KW - landmeetkunde KW - wiskunde KW - fysica KW - geometrie UR - https://www.unicat.be/uniCat?func=search&query=sysid:131515549 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 -