  We obtain new gauge-invariant forms of two-dimensional integrable systems of
nonlinear equations: the Sawada-Kotera and Kaup-Kuperschmidt system, the
generalized system of dispersive long waves, and the Nizhnik-Veselov-Novikov
system. We show how these forms imply both new and well-known two-dimensional
integrable nonlinear equations: the Sawada-Kotera equation, Kaup-Kuperschmidt
equation, dispersive long-wave system, Nizhnik-Veselov-Novikov equation, and
modified Nizhnik-Veselov-Novikov equation. We consider Miura-type
transformations between nonlinear equations in different gauges.
