Solitons in electrical networks

Article By:

Li, Xiaofeng School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts.

Ricketts, David S. Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania.

Ham, Donhee School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts.

Last reviewed:2008

DOI:https://doi.org/10.1036/1097-8542.YB084580

Solitons are a unique class of pulse-shaped waves that propagate in nonlinear dispersive media, that is, media whose response to a disturbance is not proportional to the disturbance's amplitude (nonlinearity), and in which the speed of propagation of a wave depends on its frequency (dispersion). In the course of propagation, the soliton's wave energy remains confined within its fixed pulse shape without dispersing, and the soliton exhibits other remarkable nonlinear dynamics. The first reported soliton (by John Scott Russell in 1834) was a monopulse water wave in a narrow canal where the shallow water possessed both nonlinearity and dispersion. Other examples of solitons include vibrations in nonlinear spring-mass lattices, acoustic waves in plasmas, optical pulses in fiber-optic cables, and fluxons in superconducting Josephson junctions. In long Josephson junctions, the Josephson phase satisfies the sine-Gordon equation which has soliton solutions. Such soliton solutions are called fluxons as each soliton corresponds to the situation in which the supercurrent circulates around the center of the soliton and a single magnetic flux quantum is trapped in it. Indeed, solitons are found throughout nature in situations where a fine balance between nonlinearity and dispersion is achieved. Dispersion alone would flatten out a pulse-shaped wave during its course of propagation as different Fourier components of the wave would travel at different speeds. Nonlinearity, however, can counteract dispersion by making the pulse steepen and even topple over and break, as would be observed in the water waves approaching the seashore.

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