Direct and Inverse Methods in Nonlinear Evolution Equations

Robert M. Conte

ISBN 10: 3540200878 / ISBN 13: 9783540200871

Published by Springer Berlin Heidelberg Okt 2003, 2003

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables.The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved. 292 pp. Englisch.

Seller Inventory # 9783540200871

Bibliographic Details

• Title: Direct and Inverse Methods in Nonlinear Evolution Equations
• Publisher: Springer Berlin Heidelberg Okt 2003
• Publication Date: 2003
• Language: English
• ISBN 10: 3540200878
• ISBN 13: 9783540200871
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 21D millimeters 241 millimeters width by 160 millimeters height by 21 millimeters depth
• Weight: 606 grams

About this title

Synopsis

Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables.
The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved.