Filotea Crasovan Neacsu


My dear English readers, have you ever been on a boat? The route starts at the nearest deck from your home. Now, we know that we are crossing a river, but do we really know where we are headed? To the final stop: a canal, specifically the Union Canal of Scotland. Imagine we were in the same circumstances and struggling on the same boat two centuries ago. People with that kind of endeavours were either individuals from the royal scot or scientific passionates, just as John Scott Russell. In 1834, this naval architect and civil engineer made history: he was the first one to observe the presence of solitary waves.


When I was a kid my dad used to tell me a story, the fascinating story of the never-breaking waves he was investigating in the photonics lab of ICFO (Institut de Ciències Fotòniques) [1]. The scope of their team was to discover under which conditions optical stationary waves could form and for which parameters these stationary waves were robust enough to make them good candidates for optical communications. These extremely robust waves are called either solitary waves or solitons. His passion was to perform numerical simulations of waves that lead to further laboratory investigations. My aim here is to briefly introduce you to the wonderful world of solitary waves. 

Physicists are most commonly known for their ability to unravel secrets by observing natural phenomena. The first to welcome this kind of waves was John Russell, it all happened while a boat was suddenly drawn in a canal. At that moment, the mass of water from the narrow channel was put into motion and began to transform its surface into a rounded elevation. As he was riding a horse, he overtook the trajectory at a speed of nine miles per hour. It’s interesting to point out the height of the wave, which nearly reached a foot and a half, and only diminished after two miles [2, 3, 4].

While John Russell was studying the water surface of a lake, he designed a fashioned way to describe waves with different orders, which were compiled into the System of Water Waves. He also acknowledged that when the velocity of air was greater than a mile per hour, water became less capable of reflecting light. So, we arrived at the wave of interest, a first-order wave.. A more graphic example of the so-called wave of translation is imagining a wave so great in length that one end touches Aberdeen while the other may reach the Thames [2, 5]

Solitary waves might also be generated by a vessel travelling at supercritical speeds. The speed of the wave depends on its size and the width on the depth of the water it is travelling in. Solitary waves are stable, and can travel over very large distances (normal waves would tend to either flatten out, or steepen and topple over). Unlike normal waves, solitary waves will never merge – so a small wave is overtaken by a large one, rather than the two combining. This also holds for two solitons moving in opposite directions: they simply cross each-other without shape distortion (see Fig. 1), and due to this particle-like behaviour they got the “on” suffix in their names (similar to electrons, protons…). If a wave is too big for the depth of water, it splits into two, one big and one small.

Figure 1: These three pictures depict the captivating propagation of solitons. In this case, we have set an example in which two different solitons (a) travel in opposite directions along a physical surface.  Later on, they meet each other (b) in such a way that they do not change their silhouette, they only suffer an extremely subtle disturbance. Finally, they continue forward with their trajectory (c).

We may also take a biology perspective, it is intriguing how behind proteins and nucleotide pieces, which constitute a low-frequency collective, we may also find solitons [6, 7]. In the area of neuroscience it has been proposed a model in which electrical connections within and between neurons happen thanks to solitary waves [8, 9]. These kinds of waves are one of the greatest candidates for nature, because they are characterised by little dissipation. Lipids that form our cell nerve membranes can display melting transitions at temperatures of physiological interest (that’s to say, temperatures at which take place trascendental processes within our organism, such as enzymatic denaturalization), the compressibility of which is defined as nonlinear functions of temperature and pressure. This feature leads to the possibility of soliton propagation in such membranes under the influence of action potential [10]

Other interesting examples can also be found in chemistry. The soliton phenomenon can be illustrated in polyacetylene polymer chains. In their state of equilibrium, a polyacetylene chain will alternate single and double bonds. The fact is that when achieving two consecutive single bonds, the chain experiences an excitation which can propagate along the chain by electronic and nuclear rearrangements. Due to fundamental laws, during their propagation these excitations cannot undergo deformation or mitigation. However, if two excitations in soliton form collide, they could dissipate their energy into other systems. [11]


References

[1] Optical solitons. Group research interests. ICFO Available from:  https://www.icfo.eu/interest/6/optical-solitons/3/ [Accessed 16th February 2022]

[2] Scott Russell, J. (1845). Report on Waves: Made to the Meetings of the British Association in 1842–43.  

[3] Gardner, Clifford S.; Greene, John M.; Kruskal, Martin D.; Miura, Robert M. (1967). Method for Solving the Korteweg–deVries Equation. Physical Review Letters. 19: 1095–1097. Bibcode:1967PhRvL..19.1095G. Available from: https://doi:10.1103/PhysRevLett.19.1095  

[4] Remoissenet, M. (1999). Waves called solitons: Concepts and experiments. Springer. p. 11. ISBN 9783540659198.

[5] G. G. Rozenman, A. Arie, L. Shemer (2019). Observation of accelerating solitary wavepackets. Phys. Rev. E. 101 (5): 050201. Available from: https:/doi:10.1103/PhysRevE.101.050201. 

[6] Davydov, Aleksandr S. (1991). Solitons in molecular systems. Mathematics and its applications (Soviet Series). Vol. 61 (2nd ed.). Kluwer Academic Publishers. ISBN 978-0-7923-1029-7.

[7] Yakushevich, Ludmila V. (2004). Nonlinear physics of DNA (2nd revised ed.). Wiley-VCH. ISBN 978-3-527-40417-9.

[8] Heimburg, T., Jackson, A.D. (12 July 2005). On soliton propagation in biomembranes and   nerves. Proc. Natl. Acad. Sci. U.S.A. 102 (2): 9790–5. Available from: http://doi:10.1073/pnas.0503823102. PMC 1175000. PMID 15994235.

[9] Heimburg, T., Jackson, A.D. (2007). On the action potential as a propagating density pulse and the role of anesthetics. Biophys. Rev. Lett. 2: 57–78. arXiv:physics/0610117. Bibcode:2006physics..10117H. Available from: http://doi:10.1142/S179304800700043X. S2CID 1295386.

[10] Andersen, S.S.L., Jackson, A.D., Heimburg, T. (2009). Towards a thermodynamic theory of nerve pulse propagation. Prog. Neurobiol. 88 (2): 104–113. Available from: http://doi:10.1016/j.pneurobio.2009.03.002. 

[11] Laughlin, R.B. (1999). Nobel lecture:Fractional quantization. Reviews of Modern Physics 71 (4). pp.864-865.

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