Zero curvature connections in a principal bundle are introduced. It is shown that such connections are very useful in formulating the Bäcklund problem and in constructing transformations. A general technique can be proposed for producing such transformations by defining the relevant connection coefficients appropriately. Finally, several applications of this work to various types of nonlinear partial differential equations will be presented.
Bracken, Paul. "Connections of zero curvature and Bäcklund transformations." International Journal of Pure and Applied Mathematics 100.1 (2015): 95-108. doi.org/10.12732/ijpam.v100i1.9
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International Journal of Pure and Applied Mathematics