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    Abundant solitary wave solutions to a perturbed Schrödinger equation with Kerr law nonlinearity via a novel approach
    (Elsevier B.V., 2022) Aldhabani, M.S.; Nonlaopon, K.; Rezaei, S.; S.Bayones, F.; Elagan, S.K.; El-Marouf, S.A.A.
    The main purpose of the present paper is to introduce a reliable method, for the first time, in solving differential equations with partial derivatives. The significant idea behind this method is the modification of a well-known method. The main base functions used in the solution's structures are Jacobi elliptic functions which are known functions and have many applications in practice. In order to achieve these results, the perturbed Schrödinger equation with Kerr law nonlinearity is considered. This nonlinear equation illustrates the propagation of optical solitons in nonlinear optical fibers. Thereupon, several analytical solutions corresponding to this model are obtained through employing an improved generalized exponential rational function method. Then we present a new version of it that is presented for the first time in the literature. Using these methods, several wave solutions related to the considered model are obtained. Moreover, several numerical simulations relevant to the resulting solutions are performed in the paper. As a notable features of the proposed method, the obtained solutions are characterized by the Jacobi elliptic functions. These solutions contain an index that for some specific choices is reduced to standard functions such as trigonometric and hyperbolic. The obtained results and solutions can be used for investigating the mechanism of several nonlinear phenomena laboratory and space plasmas. All necessary calculations are performed via symbolic packages of Wolfram Mathematica. © 2022 The Authors
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    Some optical solutions to the higher-order nonlinear Schrödinger equation with Kerr nonlinearity and a local fractional derivative
    (Elsevier B.V., 2022) Nonlaopon, Kamsing; Kumar, Sachin; Rezaei, S.; Bayones, Fatimah S.; Elagan, S.K.
    Partial differential equations are among the most important mathematical tools for scientists in describing many physical and engineering problems related to real life. Accordingly, in this work, an efficient technique is proposed for getting different collections of solutions to a third-order version of nonlinear Schrödinger's equation. Some numerical simulations related to the acquiblack solutions are also provided in this research. All results presented in this article can be consideblack as new achievements for the model. Further, it is emphasized that the used technique enables us to study other forms of nonlinear models. It is obtained that the technique is a reliable tool in handling many nonlinear partial differential equations arising in engineering, fluid mechanics, nonlinear optics, oceans, seas, and many mathematical physics. Moreover, the present results help the plasma physics researchers for investigating many nonlinear modulated structures that can generate and propagate in laboratory and space plasmas. © 2022 The Authors
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    A variety of closed-form solutions, Painlevé analysis, and solitary wave profiles for modified KdV–Zakharov–Kuznetsov equation in (3+1)-dimensions
    (Elsevier B.V., 2022) Nonlaopona, K.; Mann, N.; Kumar, S.; Rezaei, S.; Abdou, M.A.
    The major goal of the article is to use the generalized exponential rational function method to seek abundant closed-form solutions and dynamics of solitary wave profiles to the (3+1)-dimensional modified KdV–Zakharov–Kuznetsov (MKdV–ZK) equation. We also apply the Painlevé analysis with Kruskal simplification to investigate the integrability of the said equation. The (3+1)-dimensional MKdV–ZK model is a significant model with great advantages in various disciplines of physics, such as nonlinear optics, fluid dynamics, plasma physics, mathematical physics, and quantum mechanics. By taking advantage of the generalized exponential rational function technique, we extracted various soliton solutions, including exponential form, trigonometric form, and hyperbolic form function solutions. From both mathematical and physical points of view, it is important to obtain bright–dark soliton forms and other solitonic wave profiles. Furthermore, the results have been graphically revealed using 3D, 2D, and contour plots to demonstrate the underlying dynamics of the interactive waves. The obtained findings indicate the method's efficacy and dependability, allowing it to be widely applied in a variety of advanced nonlinear evolution equations. © 2022 The Author(s)