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  • Textbook
  • © 2003

Nonlinear Dynamics

Integrability, Chaos and Patterns

  • Covers all aspects of nonlinear dynamics in a unified and comprehensive way
  • Numerous examples and exercises will help the student to assimilate and apply the techniques presented
  • Suited to an interdisciplinary audience of physicists, engineers and other applied scientists
  • Includes supplementary material: sn.pub/extras

Part of the book series: Advanced Texts in Physics (ADTP)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XX
  2. What is Nonlinearity?

    • M. Lakshmanan, S. Rajasekar
    Pages 1-15
  3. Linear and Nonlinear Oscillators

    • M. Lakshmanan, S. Rajasekar
    Pages 17-30
  4. Qualitative Features

    • M. Lakshmanan, S. Rajasekar
    Pages 31-74
  5. Bifurcations and Onset of Chaos in Dissipative Systems

    • M. Lakshmanan, S. Rajasekar
    Pages 75-121
  6. Chaos in Dissipative Nonlinear Oscillators and Criteria for Chaos

    • M. Lakshmanan, S. Rajasekar
    Pages 123-158
  7. Chaos in Nonlinear Electronic Circuits

    • M. Lakshmanan, S. Rajasekar
    Pages 159-189
  8. Chaos in Conservative Systems

    • M. Lakshmanan, S. Rajasekar
    Pages 191-234
  9. Characterization of Regular and Chaotic Motions

    • M. Lakshmanan, S. Rajasekar
    Pages 235-258
  10. Further Developments in Chaotic Dynamics

    • M. Lakshmanan, S. Rajasekar
    Pages 259-293
  11. Finite Dimensional Integrable Nonlinear Dynamical Systems

    • M. Lakshmanan, S. Rajasekar
    Pages 295-340
  12. Linear and Nonlinear Dispersive Waves

    • M. Lakshmanan, S. Rajasekar
    Pages 341-357
  13. Korteweg—de Vries Equation and Solitons

    • M. Lakshmanan, S. Rajasekar
    Pages 359-380
  14. Basic Soliton Theory of KdV Equation

    • M. Lakshmanan, S. Rajasekar
    Pages 381-405
  15. Other Ubiquitous Soliton Equations

    • M. Lakshmanan, S. Rajasekar
    Pages 407-454
  16. Spatio-Temporal Patterns

    • M. Lakshmanan, S. Rajasekar
    Pages 455-495
  17. Nonlinear Dynamics: From Theory to Technology

    • M. Lakshmanan, S. Rajasekar
    Pages 497-521
  18. Back Matter

    Pages 523-619

About this book

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.

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)

Authors and Affiliations

  • Department of Physics and Center for Nonlinear Dynamics, Bharathidasan University, Tiruchirapalli, India

    M. Lakshmanan

  • Department of Physics, Manonmaniam Sundaranar University, Tirunelveli, India

    S. Rajasekar

Bibliographic Information

Buy it now

Buying options

eBook USD 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access