Connections defining representations of zero curvature and their Lax and Bäcklund mappings

Systems of differential forms are considered which define representations of zero curvature on specified fiber bundles through a set of structure equations. The curvature term which appears in the structure equations generates the partial differential equation. Bäcklund and Lax connections on associated bundles can also be established. This allows a unified treatment of Bäcklund transformations and Lax systems for the cases in which the differential equation appears as the curvature term in the structure equations.