Soliton

Basically a solitary, self-reinforcing, nonlinear wave (pulse) that propagates in an undistorted manner over substantial distances. It was discovered by Scottish ship architect and engineer John Scott Russell (1808-1882) in 1834 while he was conducting experiments on the Union Canal near Edinburgh, Scotland, to determine the most efficient hull design for canal boats. The following quote describes his first observations of what he called a “Wave of Translation.”

I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped — not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation.

J. Scott Russell. “Report on Waves,” Fourteenth meeting of the British Association for the Advancement of Science, 1844.

Solitary waves were not fully appreciated and were largely ignored by Russell’s contemporaries and later scientists, or were regarded merely as an interesting curiosity. It wasn’t until 1895 that Dutch mathematician Diederik J. Korteweg and his student Gustav de Vries provided the theoretical explanation in “On the Change of Form of Long Waves advancing in a Rectangular Canal and on a New Type of Long Stationary Waves; Philosophical Magazine, 5th series, vol. 36, pp. 422-443, 1895. But the real significance of Russell’s discovery in physics, electronics, biology, and especially fiber optics had to wait until the 1960s and the advent of modern digital computers that their characteristics were more thoroughly investigated and used to study non-linear wave propagation and to model various physical conditions leading to the modern general theory of solitons.

solitons (that they are localized and preserved under collisions) leads to a large number of applications for solitons.

Today, largely because of their particle-like behavior, solitons are used as a constructive element to formulate the complex dynamic behavior of wave systems in almost all facets of science, including hydrodynamics, nonlinear optics, plasmas, shock waves, and tornados. Solitons are also used to model high temperature superconductors and energy transport in DNA, as well as to assist in the development of new mathematical techniques and concepts underpinning further non-linear, wave-like developments, such as the application of solitary waves in fiber-optic communications networks.

For a practical guide to the fascinating world of solitons that appeals to an interdisciplinary readership of chemists, engineers, and physicists, see: Michel Remoissenet. Waves Called Solitons: Concepts and Experiments. New York: Springer-Verlag, 1994. And for a detailed review of nonlinear science including solitons and Chaos Theory, see: Alwyn C. Scott. Nonlinear Science: Emergence and Dynamics of Coherent Structures. Oxford University Press, 2003. For a shorter but not too much less detailed treatment perfect for those trained in mathematics that deals directly with the significance of Russell’s contributions to science, see Scott’s paper: “The Development of Nonlinear Science,” given at the University of New Mexico, Department of Physics and Astronomy, Consortium of the Americas Seminars, October 10, 2005, published in Rivista del Nuovo Cimento, Vol, 27, No. 10-11, pp. 1-115, DOI:  10.1393/ncr/i2005-10001-3. If you enjoy high level mathematics, you may want to take a look at Alex Kasman’s very interesting and instructive soliton web page: http://kasmana.people.cofc.edu/SOLITONPICS/.

Author’s Note: Until recently, Russell was best remembered in the scientific community for his considerable successes in ship hull design and for conducting the first experimental study of the Doppler shift of sound frequency as a train passes. It is entirely appropriate that a fiber-optic cable connecting Edinburgh and Glasgow now runs beneath the very canal tow-path along which John Scott Russell made his initial observations of the soliton.