Vol. 33, Issue 2-3, pp. 539-546 (2003)

Abstract

We discuss some properties of the soliton equations of the type ¶ u/¶ t = S[u, u], 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.