A soliton is a solitary wave which is propagated without becoming deformed in a non-linear and dispersive medium. One finds some in many physical phenomena just as they are the solution many non-linear partial derivative equations.

The associated phenomenon was described for the first time by the Scot John Scott Russell who initially observed it while walking along a channel: it followed during several kilometers vague going up the current which did not seem to want to weaken. Thus on water, it is related with the Mascaret. It appears for example in the the Seine at certain places and certain times.

This mode of propagation of a wave on long distances explains also the propagation of the tsunami (or tidal wave). Those practically move without notorious effect out of deep water. Transport by soliton explains why the tsunami, insensitive for the ships at sea, can be born from a seism on a coast of the Pacific Ocean, and to have effects on the opposite coast.

The use of let us solitons was proposed to improve the performance of the transmissions in the optical networks of Télécommunications in 1973 by Akira Hasegawa of the Bell laboratory from AT&T. In 1988, Mollenauer Flax and its team transmit solitons on more than 4.000 km by using the Raman Diffusion, of the name of an Indian physicist who described a way of amplifying the signals in a fiberoptic. In 1991, always to Beautiful Labs, a team transmits solitons on more than 14.000 km by using amplifiers with Erbium.

In 1998, Thierry Georges and his team of the research center and development of France Telecom combine solitons different wavelengths (Multiplexage in wavelength) to carry out a transmission with an higher capacity with 1 terabit a second (1 000.000.000 000 bits a second).

In 2001, let us solitons them find an application practical with the first equipment of Télécommunications transporting real traffic on a commercial Réseau.

In 2004, NR. Sugimoto of the university of Ōsaka found the means of introducing dispersion during the wave propagation acoustics, and consequently to create the first let us solitons acoustic. A potential use of this phenomenon is the reduction of the shock waves at the entry of trains in the tunnels.

In 2006, Michael Manley observes thanks to experiments of diffusion by x-rays and Neutron S of let us solitons within crystals of Uranium brought up to an high temperature.

The theory of let us solitons especially developed thanks to the optics made non-linear thanks to the Kerr effects or of photoréfraction, the experiment and the theory shouldering itself: That is to say a plane light wave, whose intensity decrease according to the distance to a central point. Towards the center, the increase in the index of refraction which results from the increase in intensity reduces the propagation velocity and the wave becomes convergent; but this convergence is limited because of failure of geometrical optics, and the experiment as well as the resolution of the Maxwell's equations show that the essence of luminous energy is propagated in a filament surrounded by a wave évanescente. Energy being concentrated in two directions (perpendicular to the filament) and being propagated in a third, one names this filament “soliton 2+1”. The presence of a nearby filament modifies the electromagnetic field differently according to whether one is nearby or opposite side with the close filament, so that the variation resulting from the field thus of the index of refraction curves the filament. The filament can be curved in order to form a Tore, for example while posing that the magnetic permeability of the medium also grows with the field. The torus obtained is a three-dimensional soliton (3+0) which can represent a particle. These particles have all the properties of the material particles: their interactions by their fields évanescents allow, in particular, of the interferences.

In theory (quantum) of the fields, the let us solitons topological are noncommonplace traditional solutions topologically. They bear various names according to whether they minimize the Action (- > instanton ) or energy, and according to respective topologies of the space and the group of gauge ( monopoly , vortex , skyrmion , '' strand '',…).

The equation of sine-Gordon

The nonlinear equation of Schrödinger

External bonds

See also Mathematical | Physical