  We discuss some properties of the soliton equations of the type, partial
derivative u/partial derivative t = S [u, (u) over bar], where S is a nonlinear
operator differential in x, and present the additivity theorems of the class of
the soliton equations. On using the theorems, we can construct a new soliton
equation through two soliton equations with similar properties. Meanwhile,
exact N-envelope-soliton solutions of the Hirota equation are derived through
the trace method.
