Contact Geometry and Nonlinear Differential Equations Kushner Lychagin Rubtsov

Contact Geometry and Nonlinear Differential EquationsAuthor(s): Alexei Kushner, Valentin Lychagin, Vladimir Rubtsov\nFormat: Hardback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9780521824767, 978-0521824767\nSynopsis\nMethods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be app.