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Abstract:In this communication, we use a compact split step Padé scheme (CSSPS) to solve the scalar higher-order nonlinear Schrödinger equation (HNLS) with higher-order linear and nonlinear effects. The second part, consisting of two sections, the first section is dedicated to the study numerically the stabilization of high-order solitons dynamic in optical fibers by compensation or by the interplay of higher order nonlinearity -especially quintic nonlinearityand the self-steepening. In the second section we study also numerically the propagation of conventional chirped or unchirped solitons in optical fibers with to the management of the nonlinearity, dispersion and loss (gain).Keywords: higher order optical solitons, compact split step Padé scheme, higher-order nonlinear Schrödinger equation (HNLS), quintic nonlinearity, dispersion managed. Introduction:Propagation of solitons in optical fibers has attracted a great attention of many authors [1][2][3]. The balance between nonlinear Kerr effect and chromatic dispersion is the clue of the stability of optical NLS solitons [2]. The propagation of ultra-short and ultra-intense optical solitons in optical fibers is not so obvious and requires efficient and fast numerical methods in order to be investigated. At high power higher order nonlinearities may alter the propagation of the solution especially with the interplay of higher order dispersion effects such as third or fourth ordered dispersion. Quintic nonlinearity [4] is the most important nonlinear effect due to the saturation of optical field [5] and must be taken into account in the study of ultra-intense optical solitons. In this communication we use a compact split step Padé scheme (CSSPS) [6] to solve the higher-order nonlinear Schrödinger (HNLS) equation with power law nonlinearity [7,8] and higher order dispersion effects, in order to study numerically the impact of the combined nonlinear effects, such self-steepening and quintic nonlinearity on the propagation of the higher-order soliton in optical fibers, and the evolution of conventional unchirped or chirped solitons in optical fibers with to the management of the nonlinearity, dispersion and loss (gain).

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