Bilinear equations, Bell polynomials and linear superposition principle

Abstract

A class of bilinear differential operators is introduced through assigning appropriate signs and used to create bilinear differential equations which generalize Hirota bilinear equations. The resulting bilinear differential equations are characterized by a special kind of Bell polynomials and the linear superposition principle is applied to the construction of their linear subspaces of solutions. Illustrative examples are made by an algorithm using weights of dependent variables.