Soliton

In mathematics and physics, a soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity. Solitons are caused by a 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 are the solutions of a widespread 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 name was coined by Zabusky and Kruskal to describe solutions to the Korteweg–de Vries equation which models waves of the type seen by Russell, with the name meant to refer to the solitary nature of the waves and the 'on' suffix mirroring the usage for particles such as electrons, baryons or hadrons, due to the observed 'particle-like' behaviour of the waves in which they collide, then emerge from the interaction seemingly unchanged. A single, consensus definition of a soliton is difficult to find. ascribe three properties to solitons: They are of permanent form; They are localized within a region; They can interact with other solitons, and emerge from the collision unchanged, except for a phase shift. More formal definitions exist, but they require substantial mathematics. Moreover, some scientists use the term soliton for phenomena that do not quite have these three properties (for instance, the 'light bullets' of nonlinear optics are often called solitons despite losing energy during interaction). Dispersion and nonlinearity can interact to produce permanent and localized wave forms. Consider a pulse of light traveling in glass. This pulse can be thought of as consisting of light of several different frequencies. Since glass shows dispersion, these different frequencies travel at different speeds and the shape of the pulse therefore changes over time.