Pseudopotentials of Estabrook and Wahlquist, the Geometry of Solitons, and the Theory of Connections

Abstract

The prolongation structure of Wahlquist and Estabrook is interpreted as a connection. In this way, some geometric insight might be provided for the description of those nonlinear partial differential equations which admit soliton solutions. A new geometric property—linked to the existence of an $\mathrm{SL}(2, R)$ connection—is proved for the solutions of the Korteweg-de Vries equation.