The Versatile Soliton

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.

List of contents

An Early History of the Soliton.- A Century and a Half Ago.- The Great Solitary Wave of John Scott Russell.- Relatives of the Soliton.- Nonlinear Oscillations and Waves.- A Portrait of the Pendulum.- From Pendulum to Waves and Solitons.- The Present and Future of the Soliton.- Frenkel's Solitons.- Rebirth of the Soliton.- Modern Solitons.

Summary

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.

Additional text

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 levelthe reader is supposed to follow some mathematical computations.” (Dmitry Shepelsky, Zentralblatt MATH, Vol. 1205, 2011)

Report

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 levelthe reader is supposed to follow some mathematical computations." (Dmitry Shepelsky, Zentralblatt MATH, Vol. 1205, 2011)

Product details

• Authors: Alexandre T Filippov, Alexandre T. Filippov
• Publisher: Springer, Basel
• Languages: English
• Product format: Paperback / Softback
• Released: 04.01.2011
• EAN: 9780817649739
• ISBN: 978-0-8176-4973-9
• No. of pages: 261
• Dimensions: 157 mm x 15 mm x 235 mm
• Weight: 429 g
• Illustrations: XVII, 261 p. 77 illus.
• Series: Modern Birkhäuser Classics; Modern Birkhauser Classics; Modern Birkhäuser Classics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis