Solitary wave

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In mathematics and physics, a solitary wave can refer to

• The solitary wave (water waves) or wave of translation, as observed by John Scott Russell in a barge canal in 1834. It is the prototype for a soliton.
• A soliton, a generalization of the wave of translation to general systems of partial differential equations.
• A topological defect, a generalization of the idea of a soliton to any system which is stable against decay due to homotopy theory.

The name soliton appears to have been coined by Norman Zabusky and Martin Kruskal. However, the name solitary wave—as used in the propagation of non-dispersive energy bundles through discrete and continuous media—is more general, irrespective of whether the Korteweg–de Vries equation (KdV equation), sine-Gordon equation, non-linear Schrödinger equation, Toda field theory or some other equation which allows for solitary wave solutions is used.

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