Contact Geometry and Nonlinear Differential Equations by Alexei Kushner
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Contact Geometry and Nonlinear Differential Equations
By Alexei Kushner

Contact Geometry and Nonlinear Differential Equations

By (author) See other recent books by Alexei Kushner See other recent books by Valentin Lychagin See other recent books by Vladimir Rubtsov
Format: Hardback

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Contact Geometry and Nonlinear Differential Equations by Alexei Kushner

Book Description

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).

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Book Details

ISBN: 9780521824767
ISBN-10: 0521824761
Format: Hardback
(234mm x 156mm x 32mm)
Pages: 518
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 21-Dec-2006
Country of Publication: United Kingdom

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Author Biography - Alexei Kushner

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

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