Exact bright and dark solitary wave solutions of the generalized higher-order nonlinear Schrödinger equation describing the propagation of ultra-short pulse in optical fiber

Considering linear and nonlinear optical effects like group velocity dispersion, higher-order dispersion, Kerr nonlinearity, self-steepening, stimulated Raman scattering we obtain a higher-order nonlinear Schrödinger equation describing the propagation of ultra-short pulse in optical fiber. We construct exact bright and dark solitary wave solutions of the generalized obtained equation, obeying to some constraint relations between coefficient's equation via the Bogning-Djeumen Tchaho-Kofané method (BDKm). The generalized higher-order nonlinear Schrödinger equation is obtained by affecting coefficients n i ( i = 0, 1, .., 5) to different terms of non modified equation. New solutions are obtained, and the term or higher-order dispersion can be considered as the new selector of solitary wave-type propagating in the higher-order nonlinear optical fiber.