J. F. Alzaidi

Bio: J. F. Alzaidi is an academic researcher from King Khalid University. The author has contributed to research in topics: Nonlinear system & Boundary value problem. The author has an hindex of 5, co-authored 11 publications receiving 84 citations.

Sub-10-fs-pulse propagation between analytical and numerical investigation

Abstract: This paper investigates the analytical solutions of the well-known nonlinear Schrodinger (NLS) equation with the higher-order through three members of Kudryashov methods (the original Kudryashov method, modified Kudryashov method, and generalized Kudryashov method). The considered model is also known as the sub-10-fs-pulse propagation model used to describe these measurements’ implications for creating even shorter pulses. We also discuss the problem of validating these measurements. Previous measurements of such short pulses using techniques. This paper’s aim exceeds the idea of just finding the traveling wave solution of the considered model. Still, it researches to compare the used schemes’ accuracy by applying the quintic-B-Spline scheme and the convergence between three methods. Many distinct and novel solutions have been obtained and sketched, along with different techniques to show more details of the model’s dynamical behavior. Finally, the matching between analytical and numerical schemes has been shown through some tables and figures.

Computational and approximate solutions of complex nonlinear Fokas–Lenells equation arising in optical fiber

Abstract: This manuscript uses the generalized Khater (GK) method and the trigonometric quintic B-spline (TQBS) scheme to study the calculations and approximate solutions of complex nonlinear Fokas–Lenells (FL) equations. This model describes the propagation of short pulses in optical fibers. Many novel computing solutions have been obtained. The absolute, real, and imaginary values of some solutions are plotted in two three-dimensional and density graphs to explain the dynamic behavior of short pulses in the fiber. The use of constructed analytical solutions to evaluate initial and boundary conditions allows the application of numerical solutions to study the accuracy of our novel computational techniques. The performance of both methods demonstrates the ability, effectiveness, and ability to apply them to different forms of nonlinear evolution equations to check the accuracy of analytical and numerical solutions.

Bright–Dark Soliton Waves’ Dynamics in Pseudo Spherical Surfaces through the Nonlinear Kaup–Kupershmidt Equation

Abstract: The soliton waves’ physical behavior on the pseudo spherical surfaces is studied through the analytical solutions of the nonlinear (1+1)–dimensional Kaup–Kupershmidt (KK) equation. This model is named after Boris Abram Kupershmidt and David J. Kaup. This model has been used in various branches such as fluid dynamics, nonlinear optics, and plasma physics. The model’s computational solutions are obtained by employing two recent analytical methods. Additionally, the solutions’ accuracy is checked by comparing the analytical and approximate solutions. The soliton waves’ characterizations are illustrated by some sketches such as polar, spherical, contour, two, and three-dimensional plots. The paper’s novelty is shown by comparing our obtained solutions with those previously published of the considered model.

New optical solitary wave solutions of Fokas-Lenells equation in optical fiber via Sine-Gordon expansion method

Abstract: This article presents soliton solutions to a generalized nonlinear Fokas-Lenells equation via the Sine-Gordon expansion method. To uncover the clear picture of the gained solutions, the two and three-dimensional figures for the solutions are given. It is shown that the proposed methodology provides powerful mathematical tools for obtaining the exact traveling wave solutions of different nonlinear evolution equations.

On semi analytical and numerical simulations for a mathematical biological model; the time-fractional nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation

Abstract: Through five latest numerical schemes (Adomian decomposition (AD), El Kalla (EK), cubic B - spline (CBS), expanded Cubic B-Spline (ECBS), exponential cubic B - spline (ExCBS), this manuscript examines semi-analytical and numerical solutions of the time-fractional nonlinear Kolmogorov–Petrovskii–Piskunov (KPP) equation Using the Caputo–Fabrizio fractional derivative and expanded Riccati - expansion process in Hamed et al(2020) [1], developed computational solutions are investigated to determine the sufficient conditions for the implementation of the above-suggested schemes In combustion theory, mathematical biology, and other study fields, the quasi-linear model is parabolic in simulating specific reaction-diffusion systems The model’s solution represents the proliferation of a favored gene, and moving waves are pursued by nonlinear interaction By measuring the absolute error between the exact and numerical solutions, the obtained numerical solutions’ consistency is examined To explain the correspondence between the exact and numerical solutions, several sketches are given

Some optical soliton solutions to the perturbed nonlinear Schrödinger equation by modified Khater method

Abstract: This paper investigates the analytical solutions of the perturbed nonlinear Schrodinger equation through the modified Khater method. This method is considered one of the most recent accurate analytical schemes in nonlinear evolution equations where it obtained many distinct forms of solutions of the considered model. The investigated model in this paper is an icon in quantum fields where it describes the wave function or state function of a quantum-mechanical system. The physical characterization of some obtained solutions in our study is explained through sketching them in two- and three-dimensional contour plots. The novelty of our study is clear by showing the matching between our solutions and those that have been constructed in previously published papers.

Analytical versus numerical solutions of the nonlinear fractional time–space telegraph equation

Abstract: In this paper, the stable analytical solutions’ accuracy of the nonlinear fractional nonlinear time–space telegraph (FNLTST) equation is investigated along with applying the trigonometric-quantic-B...

New optical solitons of perturbed nonlinear Schrödinger-Hirota equation with spatio-temporal dispersion

Abstract: The perturbed nonlinear Schrodinger–Hirota equation with spatio-temporal dispersion (PNSHE-STD) which governs the propagation of dispersive pulses in optical fibers, is investigated in this study using an improved Sardar sub-equation method. The Kerr and power laws of nonlinearity are taken into account. As a result of this improved technique, many constraint conditions required for the existence of soliton solutions emerge. We retrieved several solutions such as the bright solitons, dark solitons, singular solitons, mixed bright–dark solitons, singular-bright combo solitons, periodic, and other solutions. Furthermore, we demonstrate the dynamical behaviors and physical significance of these solutions by using different parameter values.