The Wave That Refused to Die

In August 1834 a barge on a Scottish canal stopped, and the heap of water at its bow did not. It rolled on by itself, keeping its shape, and the man who saw it followed it on horseback. Dr. George Egely retold the scene because, in his view, nature was showing something the physics of the day forbade.

This time Dr. György (George) Egely tells a story from the history of physics. It opens the chapter “A szolitonkeltés szigorú szabályai” (“The strict rules of making solitons”) in his book Borotvaélen (“On the Razor's Edge”, 2002), and it is where his argument about waves begins.

THE RECORDA barge stops, its wave goes on

As Egely tells it (p. 35), a Scottish hydraulic engineer, John Scott Russell, was riding along the bank of a narrow navigation canal in August 1834 while two horses pulled a barge at quite a speed. When the barge hit an obstacle and stopped, the water heaped up at its bow suddenly broke away from it and set off forward on a life of its own. What was unusual was that this solitary wave travelled on for a long time in the same shape and at the same speed. Instead of dying away like ordinary waves, it kept going for kilometres, though its height slowly fell. After a chase of a few miles Russell lost sight of it, but the phenomenon gave him no rest.

The two accounts agree on the scene. Russell gives no cause for the stop, though: the boat “suddenly stopped”, and the obstacle appears only in Egely's retelling. Russell's chase was one or two miles; Egely writes of a few.

The channel. Russell did not leave it at the chase. In Egely's account he began experimenting: he built a long, narrow channel filled with water and managed to produce these solitary waves on purpose, their height falling only very slowly. In his 1844 report Russell also gave a rule for their speed, and Egely prints it beside his own drawing of such an experiment: c = √(g(h+a)), where h is the depth of the still water and a the height of the crest. A taller wave of this kind runs faster.

Background. Many thousands had probably seen such a wave before, Egely adds, on the long canals of China and France. The historian David Pritchard, in a 2025 study of Russell's canal experiments, places the observation in a run of fast-boat trials on the Scottish canals and notes that in 1834 Russell was a lecturer in mathematics and natural philosophy, not yet a professional engineer. Heriot-Watt University places the scene on the Union Canal at Hermiston, on the edge of Edinburgh.

EGELY'S NOTESWhy it should have broken

Why was the wave strange? Egely's answer (pp. 36–37) starts from two ways a travelling wave changes its shape. In a large wave the taller parts move faster than the lower ones, so the crest hurries ahead of its base: one side grows steeper, the other flatter, until the front stands vertical and the top tumbles over “like a waterfall”. The surfers who ride under breaking waves, he writes, show this nonlinearity at its finest; such waves cannot be stable. Small waves do the opposite: as they travel they grow flatter and wider until they die away, the process he calls dispersion. In a large wave the two effects can, “in a lucky case”, cancel each other, and the wave keeps roughly the same shape while its height slowly falls. That is the kind of wave Russell chased, and it is what physics now calls a soliton.

Three effects, not two. His wording needs one clarification. In a real wave three effects are at work: nonlinearity makes the wave steeper; dispersion, in today's sense, can spread it out, because wave components of different lengths travel at different speeds; friction takes energy away. Egely treats the second as an effect of the third (“friction, that is, dispersion”). In today's textbook account the balance that keeps a soliton's shape is between the first two, and friction is what makes a real soliton slowly lose height, as Russell's did.

His history of the theory is short (pp. 37–38). From 1845 the English astronomer George Airy could say something about how waves travel: he understood why large waves steepen and collapse, but by his theory such waves in shallow water must collapse. In 1876 Lord Rayleigh resolved the apparent contradiction: dispersion offsets the hurrying crest, so the shape stays. In 1895 two Dutch mathematicians, Diederik Korteweg and Gustav de Vries, wrote down the differential equation of the phenomenon for water waves. But this equation, Egely writes, could not be solved for decades, and so it was quietly forgotten, while engineers went on meeting nonlinear effects in collapsing bridges, torn aircraft wings and distorting amplifiers. Physicists kept to the linear world, in his view, because struggling with nonlinear phenomena was simply not “fashionable”.

The fashion for nonlinear waves, he writes, began only in the mid-1970s, when personal computers started to spread and it turned out that certain nonlinear equations can be solved: almost a hundred years after Rayleigh. The section on today, below, sets those dates against the record.

EGELY'S LENSThe strict rules

The chapter is named after the strict rules of making solitons, and this is where Egely's own interest lies (pp. 39–40). Ordinary, linear waves are almost impossible to get wrong: move a wooden plug in the water or yank it out, however clumsily, and they appear. A soliton forms only within narrow limits. His drawing shows the set-up: a small vessel set in the water, its level higher than the water around it, closed by a gate. Yank the gate up fast enough and, in a lucky case, a soliton sets off.

The rules, as he lists them: if the difference in level is small, only linear ripples leave. Above a minimum, critical level a soliton forms; raise the level beyond it and a soliton leaves with a packet of ripples behind it that slowly die away; raise it further and two solitons set off one after the other, and so on. The amount of water matters too, he adds: the reservoir must hold roughly as much as the soliton itself. He illustrates the point with dye: colour the reservoir water and, he writes, the coloured water would stay behind, because only the disturbance runs on. The physics is a little less tidy. What runs down the channel is the wave form, not one unchanging parcel of water; but the water under a solitary wave does move, and experiments show it ends up shifted a little in the direction of travel, more at the surface than at the bottom.

Why it mattered to him. The chapter belongs to a part of the book called “Tesla hullámai” (“Tesla's waves”). Egely suspected (p. 19) that Nikola Tesla's radio transmitter sent out electrical solitons rather than ordinary radio waves, and that this made it better than what came after. That is his interpretation, and we leave it for another time.

TODAYWhat the record adds

The 1895 equation. The paper by Diederik Korteweg and Gustav de Vries announces in its title “a new type of long stationary waves”: the two authors already gave the solution for a single wave of steady shape, of Russell's kind, and the French engineer Joseph Boussinesq had explained Russell's wave in theory in 1871, five years before Rayleigh. What came much later was something different: a method for solving the equation's initial-value problem. In 1967 Clifford Gardner, John Greene, Martin Kruskal and Robert Miura showed how to calculate the evolution of a starting shape that levels off quickly enough on either side, a class of cases that includes shapes which break up into several solitons.

The fashion. The word “soliton” itself was coined in 1965 by Norman Zabusky and Martin Kruskal, who followed such waves in computer calculations and found that they pass through one another and come out unchanged, like particles. That was about a decade before the personal computers Egely names. Pritchard uses Egely's own word: solitary waves “re-entered fashion in the 1960s”.

Airy and the canal. Pritchard's reading of the record agrees with Egely on Airy: in 1845 Airy acknowledged the precision of Russell's experiments but rejected his attempts at a theory, and Stokes, more politely, shared his doubts. The canal has had the last word. On 12 July 1995, mathematicians and scientists from a conference on nonlinear physics and biology lined an aqueduct of the Union Canal near Heriot-Watt University in Edinburgh, watched a boat stop suddenly and send a wave running ahead of it, and renamed the aqueduct after Russell. Solitons are not only a water phenomenon, as Egely also notes: in light, they were first observed in a glass fibre at Bell Laboratories in 1980.

EGELY'S OTHER WORKOutside the fashion

Egely's own instrument has nothing to do with water waves. What links it to this chapter is his conviction that effects outside the fashion of the day deserve a closer look. His vitality meter, still made today as the Egely Wheel, is a small wheel designed to make the connection between a person's inner state and the wheel's movement observable through direct experience. If the files in this series make you want to try it, the wheel is made and sold by us.

Sources

1. György Egely, Borotvaélen, Egely Kft., 2002, ISBN 963 202 683 7.
2. J. Scott Russell, “Report on Waves”, Report of the Fourteenth Meeting of the British Association for the Advancement of Science, York 1844, London (1845), pp. 311–390; the passage on p. 319. macs.hw.ac.uk (J. C. Eilbeck, Heriot-Watt University: the passage, the place and the 1995 re-creation)
3. D. Pritchard, “Making waves: the context and afterlife of John Scott Russell's canal experiments of 1834–1835”, Annals of Science 83(3), 473–500 (2026; online 2025), doi:10.1080/00033790.2025.2551062. doi.org
4. J. Boussinesq, “Théorie de l'intumescence liquide appelée onde solitaire ou de translation, se propageant dans un canal rectangulaire”, Comptes rendus de l'Académie des Sciences 72, 755–759 (1871); Lord Rayleigh, “On waves”, Philosophical Magazine 1, 257–279 (1876).
5. D. J. Korteweg, G. de Vries, “On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves”, Philosophical Magazine 39, 422–443 (1895).
6. N. J. Zabusky, M. D. Kruskal, “Interaction of ‘solitons’ in a collisionless plasma and the recurrence of initial states”, Physical Review Letters 15, 240–243 (1965), doi:10.1103/PhysRevLett.15.240.
7. C. S. Gardner, J. M. Greene, M. D. Kruskal, R. M. Miura, “Method for solving the Korteweg-deVries equation”, Physical Review Letters 19, 1095–1097 (1967), doi:10.1103/PhysRevLett.19.1095.
8. H.-C. Hsu, Y.-Y. Chen, H.-H. Hwung, “Experimental study of the particle paths in solitary water waves”, Philosophical Transactions of the Royal Society A 370, 1629–1637 (2012), doi:10.1098/rsta.2011.0445. doi.org
9. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers”, Physical Review Letters 45, 1095–1098 (1980), doi:10.1103/PhysRevLett.45.1095.
10. “Soliton wave receives crowd of admirers”, Nature, 3 August 1995, p. 373.
11. egelywheel.com: “Invented in 1994 by Dr. George Egely and refined over decades.” egelywheel.com

AI-assisted research, writing and illustration. Edited by Egely Wheel.