Abstract: The bilinear form and N-soliton solutions are derived for a combined AKNSCLL equation using the Hirota approach. These solutions are novel in general. The one-soliton solutions of the combined AKNS-CLL equation, AKNS equation and CLL equation were drawn. Also, the combined AKNS-CLL equation is given a different characteristic from the classical AKNS and CLL equations. The bilinear form and N-soliton solutions of combined nonlinear Schr¨odinger equation are obtained by reduction.

Key words: N-soliton solutions, combined AKNS-CLL equation, combined nonlinear Schr¨odinger equation, Hirota approach