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In mathematics and "physics," a solitary wave can refer——to

• The solitary wave (water waves)/wave of 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 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

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