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Bäcklund transform
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== History == [[File:Pseudosphere.png|thumb|Bäcklund transforms originated as transformations of [[pseudosphere]]s in the 1880s.]] Bäcklund transforms have their origins in [[differential geometry]]: the first nontrivial example is the transformation of [[pseudospherical surface]]s introduced by [[Luigi Bianchi|L. Bianchi]] and [[Albert Victor Bäcklund|A.V. Bäcklund]] in the 1880s. This is a geometrical construction of a new pseudospherical surface from an initial such surface using a solution of a [[linear differential equation]]. Pseudospherical surfaces can be described as solutions of the [[sine-Gordon equation]], and hence the Bäcklund transformation of surfaces can be viewed as a transformation of solutions of the sine-Gordon equation.
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