Bäcklund and Darboux Transformations: Frontmatter

By C. Rogers, Wolfgang K. Schief. 2002

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Geometry of jet spaces and integrable systems (2010, background): “In conclusion, let us briefly discuss how the constructions of Bäcklund transformations [109, 108] and zero-curvature representations [1] are translated to the geometrical language.”
A curvature theory for discrete surfaces based on mesh parallelity (2009, background): “Nowadays one associates this part of differential geometry with the theory of integrable systems; see [9, 17].”
Darboux Transformations in Integrable Systems: Theory and their Applications to Geometry (2005, result): “Schief [90] with many recent results was published in 2002.”
Soliton solutions of an integrable nonlocal modified Korteweg-de Vries equation through inverse scattering transform (2016, background): “In physical fields, the NLS equation can characterize plenty of models in varies aspects, such as nonlinear optics [2], plasma physics [3], deep water waves [4] and in purely mathematics like motion of curves in differential geometry [5].”