  In a recent publication we proposed an extension of Hirota's bilinear
formalism to arbitrary multilinearities. The trilinear (and higher) operators
were constructed from the requirement of gauge invariance for the nonlinear
equation. Here we concentrate on the trilinear case, and use singularity
analysis in order to single out equations that are likely to be integrable. New
PDE's are thus obtained, along with others already well-known for their
integrability and for which we obtain here the trilinear expression. To appear
in the proceedings of NEEDS'94 (11-18 September, Los Alamos)
