Soliton
Solitons were subsequently found to provide stable solutions of a wide class of weakly nonlinear dispersive partial differential equations describing physical systems.
The soliton phenomenon was first described in 1834 by John Scott Russell who observed a solitary wave in the Union Canal in Scotland.
The name was meant to characterize the solitary nature of the waves, with the 'on' suffix recalling the usage for particles such as electrons, baryons or hadrons, reflecting their observed particle-like behaviour.
However, also the nonlinear Kerr effect occurs; the refractive index of a material at a given frequency depends on the light's amplitude or strength.
The soliton solutions are typically obtained by means of the inverse scattering transform, and owe their stability to the integrability of the field equations.
In 1834, John Scott Russell described his wave of translation:[nb 1][nb 2] 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.
He built wave tanks at his home and noticed some key properties: Scott Russell's experimental work seemed at odds with Isaac Newton's and Daniel Bernoulli's theories of hydrodynamics.
[4] Their contemporaries spent some time attempting to extend the theory but it would take until the 1870s before Joseph Boussinesq[5] and Lord Rayleigh published a theoretical treatment and solutions.
[1] In 1967, Gardner, Greene, Kruskal and Miura discovered an inverse scattering transform enabling analytical solution of the KdV equation.
The observation of accelerating surface gravity water wave soliton using an external hydrodynamic linear potential was demonstrated in 2019.
The GH jitter requires sophisticated, expensive compensatory solutions that ultimately makes dense wavelength-division multiplexing (DWDM) soliton transmission in the field unattractive, compared to the conventional non-return-to-zero/return-to-zero paradigm.
[19][20][21] Solitons can be described as almost lossless energy transfer in biomolecular chains or lattices as wave-like propagations of coupled conformational and electronic disturbances.
Consequently, the domain walls can be described as solitons, discrete regions of dislocations that are able to slip or propagate and maintain their shape in width and length.
[24][25][26] In recent literature, ferroelectricity has been observed in twisted bilayers of van der Waal materials such as molybdenum disulfide and graphene.
[23][27][28] The moiré superlattice that arises from the relative twist angle between the van der Waal monolayers generates regions of different stacking orders of the atoms within the layers.
The domain walls that separate these regions are composed of partial dislocations where different types of stresses, and thus, strains are experienced by the lattice.
It has been observed that soliton or domain wall propagation across a moderate length of the sample (order of nanometers to micrometers) can be initiated with applied stress from an AFM tip on a fixed region.
The soliton propagation carries the mechanical perturbation with little loss in energy across the material, which enables domain switching in a domino-like fashion.
In some physical contexts (for instance string theory) this feature can be important, which motivated the introduction of a special name for this class of solitons.
On the other hand, when gravity is added (i.e. when considering the coupling of the Born–Infeld model to general relativity) the corresponding solution is called EBIon, where "E" stands for Einstein.
