Contact Geometry and Nonlinear Differential Equations

Alexei Kushner

ISBN 10: 0521824761 / ISBN 13: 9780521824767

Editore: Cambridge University Press, 2007

Druck auf Anfrage Neuware - Printed after ordering - Methods 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 applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology). Codice articolo 9780521824767

Riassunto:

Shows novel and modern ways of solving differential equations using methods from contact and symplectic geometry.

Informazioni sugli autori: Alexei Kushner is a Professor and Dean of the Department of Mathematics and Computer Science, and a Senior Researcher at the Russian Academy of Sciences.

Valentin Lychagin is a Professor at the Institute of Mathematics and Statistics, Tromsø University, and a Senior Researcher at the Institute for Theoretical and Experimental Physics in Moscow.

Vladimir Rubtsov is a Professor at the Département de Mathématiques, Angers University, and a Senior Researcher at the Institute for Theoretical and Experimental Physics in Moscow.

Dati bibliografici

Titolo: Contact Geometry and Nonlinear Differential ...
Casa editrice: Cambridge University Press
Data di pubblicazione: 2007
Legatura: Buch
Condizione: Neu