The subsidiary elliptic-like equation and the exact solutions of the higher-order nonlinear Schrödinger equation

By using the homogeneous balance principle, the exact solutions of the subsidiary elliptic-like equation are derived with the aid of the coupled projective Riccati equations. The higher-order nonlinear Schrödinger equation describing the propagation of ultrashort pulses in nonlinear optical fibers is researched and its various exact solutions are derived by means of the simple transformation and the subsidiary elliptic-like equation mentioned above.