Searching for integrable PDE's by testing Hirota's three-soliton condition

The search for integrable PDE’s has been an active research subject with computer algebra as a necessary tool. In this paper we describe a search method based on the requirement that standard type threeand four-soliton solution exist in the bilinear formalism of Hirota. The existence on N-soliton solutions can be formulated as a requirement that a certain high degree polynomial in N x A4 variables vanishes on an affine manifold defined by N polynomials of M vi~riables each. An exhaustive search has been carried out for certain classes of typical equations and several new equations have been found.