On the generalized bilinear differential equations

By using the generalized Hirrota bilinear operators a kind of bilinear differential equations is established and examined when the linear super position principle can apply to the resulting generalized bilinear differential equations. Examples of generalized bilinear differential equations together with an algorithm using weights are computed using a 1+1 and 2+1 dimensional equations in order to shed more lights on the presented general scheme for the construction of the bilinear differential equations which posses linear subspaces of solutions.