Bilinear Equations and Resonant Solutions Characterized by Bell Polynomials

A class of bilinear differential operators is introduced by assigning specific signs to derivatives. The corresponding bilinear differential equations, containing Hirota bilinear equations as particular examples, are characterized by Bell polynomials. Resonant solutions of exponential waves are analyzed via recognizing the superposition principle using Bell polynomials. Two illustrative examples are computed by an algorithm adopting weights of dependent variables.