Nonlinear Dynamics: Integrability, Chaos and Patterns

✍ Scribed by Professor M. Lakshmanan, Dr. S. Rajasekar (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2003
• Tongue: English
• Leaves: 627
• Series: Advanced Texts in Physics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XX
What is Nonlinearity?....Pages 1-15
Linear and Nonlinear Oscillators....Pages 17-30
Qualitative Features....Pages 31-74
Bifurcations and Onset of Chaos in Dissipative Systems....Pages 75-121
Chaos in Dissipative Nonlinear Oscillators and Criteria for Chaos....Pages 123-158
Chaos in Nonlinear Electronic Circuits....Pages 159-189
Chaos in Conservative Systems....Pages 191-234
Characterization of Regular and Chaotic Motions....Pages 235-258
Further Developments in Chaotic Dynamics....Pages 259-293
Finite Dimensional Integrable Nonlinear Dynamical Systems....Pages 295-340
Linear and Nonlinear Dispersive Waves....Pages 341-357
Korteweg—de Vries Equation and Solitons....Pages 359-380
Basic Soliton Theory of KdV Equation....Pages 381-405
Other Ubiquitous Soliton Equations....Pages 407-454
Spatio-Temporal Patterns....Pages 455-495
Nonlinear Dynamics: From Theory to Technology....Pages 497-521
Back Matter....Pages 523-619

✦ Subjects

Statistical Physics, Dynamical Systems and Complexity;Theoretical, Mathematical and Computational Physics;Appl.Mathematics/Computational Methods of Engineering