The Versatile Soliton

  • Alexandre T. Filippov

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. An Early History of the Soliton

    1. Front Matter
      Pages 1-2
    2. Alexandre T. Filippov
      Pages 3-22
    3. Alexandre T. Filippov
      Pages 23-37
    4. Alexandre T. Filippov
      Pages 39-57
  3. Nonlinear Oscillations and Waves

    1. Front Matter
      Pages 59-60
    2. Alexandre T. Filippov
      Pages 61-94
    3. Alexandre T. Filippov
      Pages 95-128
  4. The Present and Future of the Soliton

    1. Front Matter
      Pages 129-130
    2. Alexandre T. Filippov
      Pages 131-160
    3. Alexandre T. Filippov
      Pages 161-204
    4. Alexandre T. Filippov
      Pages 205-232
  5. Back Matter
    Pages 233-261

About this book


The soliton, a solitary wave impulse preserving its shape and strikingly similar to a particle, is one of the most fascinating and beautiful phenomena in the physics of nonlinear waves.  In this classic book, the concept of the soliton is traced from the beginning of the last century to modern times, with recent applications in biology, oceanography, solid state physics, electronics, elementary particle physics, and cosmology.

The Versatile Soliton is an appropriate title indeed. There is much new historical information in the book…The book is written in a lively language and the physics presented in a clear, pedagogical style. Most of the chapters require only knowledge of fairly elementary mathematics and the main ideas of soliton physics are well explained without mathematics at all…Yet it contains valuable information and offers a historical review of soliton physics that cannot be found elsewhere. 


In summary, this book is a good elementary treatment of solitons and the related history of physics and mathematics, even for readers with little knowledge of advanced mathematics. For readers with the latter knowledge, it is still a good introduction to the physical ideas required for the understanding of solitons prior to the study of more mathematical treatments from other sources. 

—Mathematical Reviews

This engaging book is an excellent introduction into the wonderful world of soliton mechanics.  

—Zentralblatt Math

No doubt, everyone can get new information from the book. First, the book is strongly recommended to young researchers. In a certain sense, the book is unique and definitely will find a niche among numerous textbooks on solitons.  



Frenkel solitons Hermann Helmholtz John Scott Russell Particle Physics Theoretical physics nonlinear oscillations

Authors and affiliations

  • Alexandre T. Filippov
    • 1
  1. 1.Theoretical Physics, Joint Institute for Nuclear ResearchBogoliubov Laboratory ofDubnaRussian Federation

Bibliographic information