Abstract
Given an exterior differential system on a manifold M, we study general prolongations of the system on a locally trivial fiber bundle (M̃, π̃, M) by a Cartan–Ehresmann connection. We characterize such prolongations for the system associated with the KdV equation without any assumption of ‘‘(x, t) independence.’’ The partial Lie algebra discovered by Wahlquist–Estabrook [J. Math. Phys. 16, 1 (1975)] appears by this way as an intrinsic tool. Simple analytic pseudopotentials are classified up to diffeomorphism.
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