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The main aim of this paper is to conduct a detailed study on a high-order nonlinear Schrödinger (HONLS) equation involving nonlinear dispersions and the Kerr effect. More precisely, after reducing the governing model describing ultra-short pulses in optical fibers in a one-dimensional domain, its optical solitons including the bright and dark solitons are derived through the modified Kudryashov (MK) method. The dynamical behavior of the bright and dark solitons is formally investigated for different sets of the involved parameters. It is shown that increasing and decreasing nonlinear dispersions lead to significant changes in the amplitude of the bright and dark solitons. [ABSTRACT FROM AUTHOR]

• Considering a high-order nonlinear Schrödinger equation in a non-Kerr law media with the weak non-local nonlinearity. • Extracting some real and imaginary parts of the model using a wave variable transformation. • The modified Kudryashov method and symbolic computations are adopted to successfully retrieve optical solitons of the model. The present paper explores a high-order nonlinear Schrödinger equation in a non-Kerr law media with the weak non-local nonlinearity describing solitons' propagation through nonlinear optical fibers. To this end, the real and imaginary parts of the model are firstly extracted using a wave variable transformation. The modified Kudryashov method and symbolic computations are then adopted to successfully retrieve optical solitons of the model. The results presented in the current study demonstrate the great performance of the modified Kudryashov method in handling high-order nonlinear Schrödinger equations. [ABSTRACT FROM AUTHOR]

The propagation of soliton pulses in the weakly nonlocal parabolic law medium is studied in the present paper. For this objective, real and complex portions of the model that is described by a second-order nonlinear Schrödinger equation (SONLSE) are firstly extracted, then, the modified version of the new Kudryashov method (NKM) is utilized to exactly solve the resulting equation in the real regime. As a result, several optical solitons to the second-order nonlinear Schrödinger equation with weakly nonlocal and parabolic laws (WNPLs) are formally retrieved. [ABSTRACT FROM AUTHOR]

Seeking optical soliton solutions in (2+1) dimensions has achieved considerable popularity among academic researchers all around the world. The authors' purpose of the current article is to consider an integrable (2+1)-dimensional nonlinear Schrödinger system and investigate its exact solutions. As a result, a group of optical soliton solutions to the integrable nonlinear Schrödinger system in (2+1) dimensions is formally recovered using the Kudryashov method and its modified version. The dynamical features of the retrieved solitons are analyzed by providing several three-dimensional graphs. [ABSTRACT FROM AUTHOR]