Physical Sciences and Mathematics Commons^™

Connections Of Zero Curvature And Bäcklund Transformations, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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.