Resonant Solutions to (3+1)-dimensional Bilinear Differential Equations

In this thesis, we attempt to obtain a class of generalized bilinear differential equations in (3+1)-dimensions by D p-operators with p=5, which have resonant solutions. We construct resonant solutions by using the linear superposition principle and parameterizations of wave numbers and frequencies. We test different values of p in Maple computations, and generate three classes of generalized bilinear differential equations and their resonant solutions when p=5.