History Bäcklund transform

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bäcklund transforms originated transformations of pseudospheres in 1880s.


bäcklund transforms have origins in differential geometry: first nontrivial example transformation of pseudospherical surfaces introduced l. bianchi , a.v. bäcklund in 1880s. geometrical construction of new pseudospherical surface initial such surface using solution of linear differential equation. pseudospherical surfaces can described solutions of sine-gordon equation, , hence bäcklund transformation of surfaces can viewed transformation of solutions of sine-gordon equation.







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