Overview

The invertible point transformation is a powerful tool in the study of nonlinear differential and difference equations. This book gives a comprehensive introduction to this technique. Ordinary and partial differential equations are studied with this approach. The book also covers nonlinear difference equations. The connections with Lie symmetries, the Painleve property, first integrals and the Cartan equivalence method are discussed in detail. Most of the evaluations are checked with the computer language REDUCE; the book includes 30 REDUCE programs. A short introduction to the jet bundle formalism is given.Contents: First-Order Ordinary Differential EquationSecond-Order Ordinary Differential EquationsThird-Order Differential EquationsLie Point SymmetriesFirst Integrals and Differential EquationCartan Equivalence MethodPainleve Test and LinearizationPainleve Test and Partial Differential EquationsPartial Differential EquationsDifference EquationsREDUCE ProgramsJet Bundle FormalismReadership: Mathematicians, physicists and engineers.

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9781299670709

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