In mathematics, Bäcklund transforms or Bäcklund transformations (named after the Swedish mathematician Albert Victor Bäcklund) relate partial differential...

transform Z-transform Karhunen–Loève transform Affine transformation (Euclidean geometry) Bäcklund transform Bilinear transform Box–Muller transform Burrows–Wheeler...

equations are a simple example of a Bäcklund transform. More complicated, generally non-linear Bäcklund transforms, such as in the sine-Gordon equation...

Bianchi and Bäcklund led to the discovery of Bäcklund transformations. Another transformation of pseudospherical surfaces is the Lie transform introduced...

transformation, now known as auto-Bäcklund transformation. Bäcklund transform Emily Coddington Williams, translator of Bäcklund's work on non-Euclidean geometry...

Bolza surface First Hurwitz triplet Hermite constant Systoles of surfaces Systolic freedom Systolic category Envelope (mathematics) Bäcklund transform...

functions (and the transform between them) are also one of the simplest examples of a Bäcklund transform (two PDEs and a transform relating their solutions)...

The Bäcklund transform (introduced by Albert Victor Bäcklund in 1883) can be seen as the combination of a Lie transform with a Bianchi transform (introduced...

Cauchy–Kovalevskaya theorem H-principle Atiyah–Singer index theorem Bäcklund transform Viscosity solution Weak solution Loewy decomposition of linear differential...

integrable equations, to find its Lax pairs, recursion operators, Bäcklund transform, and finally finding exact analytic solutions to DE. Symmetry methods...