In mathematics and physics, a solitary wave can refer to

• The wave of translation, a solitary water wave 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 Zabusky and Martin Kruskal. However, the name solitary wave, used in the propagation of non-dispersive energy bundles through discrete and continuous media, irrespective of whether the KdV, sine-Gordon, non-linear Schrödinger, Toda or some other equation is used, is more general.

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