If you have not already heard about solitons, you will sooner or later encounter them. 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 engaging 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 main concepts and results of theoretical physics related to solitons can be explained without using much mathematics. Indeed, on the descriptive and historical level, only some knowledge of high school physics and mathematics is needed. At a higher level, for understanding the elementary theory of oscillations and waves, the reader can intuit much from the numerous illustrations and perhaps skip the formulas presented. But to appreciate the deep connections in this book between apparently different and diverse phenomena and ideas, the reader must be able to follow elementary mathematical computations. Still more advanced mathematics is required for the appendices.
From the reviews:
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. --Centaurus
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.--Physicala
The well-known author with teaching and research experience has found the right ballance between intuition, mathemtical precision and practical utility. --Acta Sci. Math.
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
"The book presents the development of the soliton theory, whose complete mathematical description is a ... refined branch of modern mathematics, as a fascinating story, full of historical collisions. ... The book emphasizes common features of diverse solitons, targeting on uncovering conceptual simplicity in apparent complexity. ... is accessible to high school students, though at this level the reader is supposed to follow some mathematical computations." (Dmitry Shepelsky, Zentralblatt MATH, Vol. 1205, 2011)
Introduction * Part I: An Early History of the Soliton * 1. A Century and a Half Ago * 2. The Great Solitary Wave of John Scott Russell * 3. Relatives of the Soliton * Part II: Nonlinear Oscillations and Waves * 4. The Equation of the Pendulum * 5. From Pendulum to Waves and Solitons * Part III: Present and Future of Solitons * 6. Frenkel's Solitons * 7. Rebirth of the Soliton * 8. Modern Solitons * Appendix I: Lord Kelvin "On Ship Waves" * Appendix II: Skyrme's Soliton * Appendix III: Mathematics * Subject Index * Name Index