Principles of Nature: towards a new visual language
Wayne Roberts © 2003-2015   

Solitons—'immortal' waves, another possible mechanism in the generation of resonant scale structures

Our general experience of waves is to see them rise then subside or 'break'. But what about waves which neither disperse nor break but continue traveling on indefinitely at the same amplitude without fading away? Do such waves exist? Yes, in fact they abound in nature. Physicists term such waves solitons.

Solitons have some remarkable properties such as being able to 'glide through one another' without 'crashing' or breaking up—each emerges from the other side of the 'collision' intact—as if each had encountered no obstruction to their passage at all!

A brief history of solitons

In 1834, John Scott Russell, an engineer by profession, was riding his horse beside an Edinburgh canal when he witnessed an astonishing natural phenomenon. Two bridled horses had been hauling a barge along the narrow canal (one on each side), which, upon stopping suddenly, caused a sudden heap of water to propel forward from the bow of the boat which, in his own words,

‘rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued on its course along the channel apparently without change of form or diminution of speed’ (J Davies, J Gribbin, 1991, p. 41)

He chased after it on his horse for two miles before eventually losing it in the meanderings of the canal. Fascinated, Russell constructed a laboratory simulation so that he could study the behaviour of wave formation and the conditions under which these special waves (later termed solitons) occurred.

His initial findings and formulae that related a wave's speed to its amplitude and to the depth of the canal were published and reported to the British Association but were virtually ignored by the establishment which considered the concept of 'solitary waves of permanent form' illogical.

More than half a century passed before Korteweg and de Vries, in 1895, extended his work in discovering an interesting nonlinear effect that contrasted with the well-known linear relation of a wave's speed (in deeper water) which was simply proportional to its wavelength. This new additional nonlinear effect, and that counterbalanced the effects of dispersion and caused a wave to 'bunch back up', came into play when a wave's height (amplitude) became comparable to the depth of water through which it was moving. In such conditions, not only do long broad waves travel faster than narrower ones, but also, taller waves travel faster than shorter waves.

Solitons occur when these opposing linear effects of dispersion are finely balanced with the concentrating effects of nonlinearity. If one of these two competing effects is lost, so too is the soliton.

There are some interesting implications which emerge from these opposing forces. Far from being improbable (we spoke of a ‘delicate balance ’), the dynamics of the situation virtually guarantees the generation of these special waves. It is only those waves in which the opposing effects of dispersion and nonlinearity are perfectly balanced which remain. All other waves are pulled off centre-stage by the tug-of-war of forces.
W. Roberts, 2003

Solitons can occur in almost any medium having the key ingredient of nonlinearity including solids, liquids, gases, fibreoptics, etc. The propensity for solitons to form, as well as their resonance in terms of longevity and balancing of opposing effects, suggests that solitons may offer yet another insight into how and why resonant scale structures form in Nature and have 'inertial-like' properties.

Soap bubbles and films

Solitons have strong conceptual ties to the concept of 'particles'; and paths of least action have equally strong ties to the concept of geodesics (the shortest distance between two points on flat or curved surfaces). Thus we have 'point', 'line', ...and naturally we might therefore expect a similar efficient class of forms relating to space and the 'plane'.

Fascinatingly, the ubiquitous bubble or soap film represents just such a surface, and is a very close relative of solitons and paths of least action. Considered together, these constitute an interesting resonant scale structure spanning a number of dimensions.

When a soap film stretches to 'join' an irregular boundary and manifests itself as a glistening twisting surface, it morphs itself holistcally into a minimal surface, a plane of minimal area and minimal net surface tension.

The shape of a spherical bubble encloses the maximum volume possible for a given surface area.

Nature thus seems to have an in-built propensity for finding or tuning-in to resonances and stable states or structures— stable by virtue of their inclusivity— that is, by taking into account all contributing factors simultaneously (e.g. the position and directional relation of every neighbouring point around the irregular but closed wire loop (see photo).

soap film

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