In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is strongly stable, in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such localized wave packets. Its remarkable stability can be traced to a balanced cancellation of nonlinear and dispersive effects in the medium. (Dispersive effects are a property of certain systems where the speed of a wave depends on its frequency.) 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 (1808–1882) who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation". The term soliton was coined by Zabusky and Kruskal to describe localized, strongly stable propagating solutions to the Korteweg–de Vries equation, which models waves of the type seen by Russell. 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.[1]
In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is strongly stable, in that it preserves its shape...
A gravitational soliton is a soliton solution of the Einstein field equation. It can be separated into two kinds, a soliton of the vacuum Einstein field...
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dispersive waves to be coupled with the solitons via the soliton trapping effect. This effect means that as the soliton self-frequency shifts to longer wavelengths...
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the nucleon by (and named after) Tony Skyrme in 1961. As a topological soliton in the pion field, it has the remarkable property of being able to model...
translation, as observed by John Scott Russell in 1834, the prototype for a soliton. A soliton, a generalization of the wave of translation to general systems of...
theory of integrable systems was revived with the numerical discovery of solitons by Martin Kruskal and Norman Zabusky in 1965, which led to the inverse...
(1997). Solitons, non-linear pulses and beams. Springer. ISBN 978-0-412-75450-0. Miroshnichenko A, Vasiliev A, Dmitriev S. Solitons and Soliton Collisions...
asymptotic analysis. His most celebrated contribution was in the theory of solitons. He was a student at the University of Chicago and at New York University...
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