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In this paper, the F-expansion method has been used to find several types of exact solutions of the higher-order nonlinear Schrödinger (HONLS) equation with cubic-quintic nonlinearities, self-steeping and self-frequency shift effects which describes the propagation of an optical pulse in optical fibers. With the aid of symbolic computation, explicit exact solutions of HONLS equation are presented which include many Jacobi elliptic function solutions, bell-shaped and kink -shaped solitary wave solutions. The properties of some solutions are shown by some figures. AMS Subject Classification: 35Q40, 35Q55, 35Q60

international journal of pure and applied mathematics

EXACT SOLUTIONS OF THE HIGHER-ORDER NONLINEAR SCHR\"{O}DINGER EQUATION WITH CUBIC-QUINTIC NONLINEARITIES, SELF-STEEPING AND SELF-FREQUENCY SHIFT EFFECTS