soliton: one construct, many systems

In hydrodynamics a soliton is a solitary wave of elevation on shallow water that travels without changing shape, because the way longer components outrun shorter ones (dispersion) is exactly cancelled by the way a taller crest moves faster (nonlinearity). Korteweg and de Vries's 1895 On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves gave the equation whose exact solution is this permanent wave, placing on a firm footing the single heaping wave John Scott Russell had chased along a canal in 1834. The referent is a self-reinforcing localised wave set by a balance of dispersion against nonlinearity, and the identical construct reappears in plasmas and in optical fibres.[1]

Unit

The amplitude and width of a shape-preserving wave, linked by the governing equation

Recovery means

Not applicable

Measured by

Identified by a pulse that propagates at constant shape and emerges unchanged after collisions, matched to the governing equation's soliton solution

In plasma physics the same construct describes localised disturbances that keep their identity and pass through one another intact, behaving so much like particles that the shape-preserving wave was given the name soliton. Zabusky and Kruskal's 1965 Interaction of "solitons" in a collisionless plasma and the recurrence of initial states discovered this particle-like persistence in numerical solutions of the same shallow-water equation applied to a plasma and coined the word. It is the identical dispersion-versus-nonlinearity balance seen in water, here realised in a collisionless plasma and recognised by the clean, memory-preserving way two such waves collide.[2]

Unit

The amplitude and speed of a particle-like wave that survives interaction

Recovery means

Not applicable

Measured by

Recognised by waves that pass through each other and recover their shapes and speeds, with only a phase shift

In nonlinear optics a soliton is a light pulse that propagates down an optical fibre without broadening, because the chromatic dispersion that would stretch it is balanced by the intensity-dependent refractive index (the Kerr nonlinearity) that compresses it. Hasegawa and Tappert's 1973 Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers predicted these pulses, and Mollenauer, Stolen, and Gordon's 1980 Experimental observation of picosecond pulse narrowing and solitons in optical fibers confirmed them. It is the same construct as the canal wave and the plasma wave, transposed into a photonic system, where it underpins soliton transmission and mode-locked fibre lasers.[3][4]

Unit

The pulse width and peak power of a non-spreading pulse, linked by the fibre's dispersion and nonlinearity

Recovery means

Not applicable

Measured by

Confirmed by a pulse that holds its width over long fibre lengths at the matching peak power predicted by the governing equation