Equations of the inverse problem Bäcklund transformations, and the theory of connections (Q1304128)

As a first step to a geometrization of the Korteweg-de Vries equation \(u_{t} + 12uu_{x} + u_{xxx}=0\), \textit{H. B. Wahlquist} and \textit{F. B. Estabrook} [J. Math. Phys. 16, No. 1, 1-7 (1975; Zbl 0298.35012)] introduced the so-called pseudopotentials as variables in some special differential forms. Later \textit{R. Hermann} [Phys. Rev. Lett. 36, No. 15, 835-836 (1976)] conjectured that those forms are connection forms in a principal bundle. In this paper the construction of \textit{R. Hermann} is revised in all details and his conjecture is proved.