Bäcklund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory

By C. Rogers, Wolfgang K. Schief. 2002

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On the solitons and nonlinear wave equations (2008, background): “We present in this section the pseudospherical reduction of the problem in the spirit of [8], [9].”
From the Real and Complex Coupled Dispersionless Equations to the Real and Complex Short Pulse Equations (2016, background): “There exists deep connections between the differential geometry and integrable nonlinear partial differential equations (PDEs) since the soliton theory was developed [34].”
Single and multi-solitary wave solutions to a class of nonlinear evolution equations (2008, methodology): “In recent decades, the circumstances changed and many powerful approaches have been devised, such as inverse scattering method [1], Darboux transformation method [2], Bäcklund transformation method [2], separation of variables method [3], Hirota bilinear method [7], Painlevé truncation expansion [8]”