A geometric formulation of Lax integrability for nonlinear equations in two independent variables

A geometric formulation of Lax integrability is introduced which makes use of a Pfaffian formulation of Lax integrability. The Frobenius theorem gives a necessary and sufficient condition for the complete integrability of a distribution, and provides a powerful way to study nonlinear evolution equations. This permits an examination of the relation between complete integrability and Lax integrability. The prolongation method is formulated in this context and gauge transformations can be examined in terms of differential forms as well as the Frobenius theorem.