Nonlinear Dynamics: Integrability, Chaos and Patterns / Edition 1

by Muthusamy Lakshmanan, Shanmuganathan Rajaseekar

Overview

Integrability, chaos and patterns are three of the most important concepts in nonlinear dynamics. These are covered in this book from fundamentals to recent developments. The book presents a self-contained treatment of the subject to suit the needs of students, teachers and researchers in physics, mathematics, engineering and applied sciences who wish to gain a broad knowledge of nonlinear dynamics. It describes fundamental concepts, theoretical procedures, experimental and numerical techniques and technological applications of nonlinear dynamics. Numerous examples and problems are included to facilitate the understanding of the concepts and procedures described. In addition to 16 chapters of main material, the book contains 10 appendices which present in-depth mathematical formulations involved in the analysis of various nonlinear systems.

Product Details

ISBN-13:	9783540439080
Publisher:	Springer Berlin Heidelberg
Publication date:	12/16/2002
Series:	Advanced Texts in Physics
Edition description:	2003
Pages:	620
Product dimensions:	6.10(w) x 9.25(h) x 0.06(d)

Table of Contents

1. What is Nonlinearity?.- 2. Linear and Nonlinear Oscillators.- 3. Qualitative Features.- 4. Bifurcations and Onset of Chaos in Dissipative Systems.- 5. Chaos in Dissipative Nonlinear Oscillators and Criteria for Chaos.- 6. Chaos in Nonlinear Electronic Circuits.- 7. Chaos in Conservative Systems.- 8. Characterization of Regular and Chaotic Motions.- 9. Further Developments in Chaotic Dynamics.- 10. Finite Dimensional Integrable Nonlinear Dynamical Systems.- 11. Linear and Nonlinear Dispersive Waves.- 12. Korteweg—de Vries Equation and Solitons.- 13. Basic Soliton Theory of KdV Equation.- 14. Other Ubiquitous Soliton Equations.- 15. Spatio-Temporal Patterns.- 16. Nonlinear Dynamics: From Theory to Technology.- A. Elliptic Functions and Solutions of Certain Nonlinear Equations.- Problems.- B. Perturbation and Related Approximation Methods.- B.1 Approximation Methods for Nonlinear Differential Equations.- B.2 Canonical Perturbation Theory for Conservative Systems.- B.2.1 One Degree ol Freedom Hamiltonian Systems.- B.2.2 Two Degrees ol Freedom Systems.- Problems.- C. A Fourth-Order Runge-Kutta Integration Method.- Problems.- Problems.- E. Fractals and Multifractals.- Problems.- Problems.- G. Inverse Scattering Transform for the Schrödinger Spectral Problem.- G.l The Linear Eigenvalue Problem.- G.2 The Direct Scattering Problem.- G.3 The Inverse Scattering Problem.- G.4 Reconstruction of the Potential.- Problems.- H. Inverse Scattering Transform for the Zakharov-Shabat Eigenvalue Problem.- H.1 The Linear Eigenvalue Problem.- H.2 The Direct Scattering Problem.- H.3 Inverse Scattering Problem.- H.4 Reconstruction of the Potentials.- Problems.- I. Integrable Discrete Soliton Systems.- I.1 Integrable Finite Dimensional N-Particles System on a Line: Calogero-Moser System.-I.2 The Toda Lattice.- I.3 Other Discrete Lattice Systems.- I.4 Solitary Wave (Soliton) Solution of the Toda Lattice.- Problems.- J. Painlevé Analysis for Partial Differential Equations.- J.1 The Painlevé Property for PDEs.- J.1.1 Painlevé Analysis.- J.2 Examples.- J.2.1 KdV Equation.- J.2.2 The Nonlinear Schrödinger Equation.- Problems.- References.

Editorial Reviews

From the reviews:

"The authors must be congratulated … . The book contains many examples, exercises and problems. … Many technical details are relegated to appendices, making the main text highly readable. … There are a large number of nice figures and illustrations, which complement the text very well. … I feel that this book would be a valuable addition to a personal or departmental library. … I believe that this book has the potential to become a standard text in the … field of non-linear dynamics." (Sanjay Puri, International Journal of Robust and Nonlinear Control, Vol. 15 (11), 2005)

"The book is an extensive treatise of nonlinear dynamical systems with emphasis on the concepts of chaos, integrability and patterns. … the book contains numerous examples and exercises divided in two groups by their difficulty." (Peter Polacik, Zentralblatt MATH, Vol. 1038 (13), 2004)

"The book gives a comprehensive introduction to the different fields in nonlinear dynamics, such as chaos, fractals, integrability and soliton theory. It also includes a large number of interesting applications. … Each chapter and the appendix include a number of exercises. … the book can be highly recommended for beginners in these fields since it provides a good survey of the different fields in nonlinear dynamics." (W.-H. Steeb, Mathematical Reviews, 2004 d)

"Undoubtedly, the best survey text on Nonlinear Dynamics available today. … the survey is carefully balanced, with detail and clarity, to enable students and researchers from other fields to learn the salient tools. For advanced undergraduate students and graduate research students looking for just one book in Nonlinear Dynamics, here is the one to get. … It is precisely the book that has been needed to provide students with the fundamental knowledge across the landscape of Nonlinear Dynamics … ." (B I Henry, The Physicist, Vol. 40 (4), 2003)

From the Publisher