S. H. Alfalqi

Bio: S. H. Alfalqi 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 10 publications receiving 53 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.

Analytically and numerically, dispersive, weakly nonlinear wave packets are presented in a quasi-monochromatic medium

Abstract: This study applies computational and numerical techniques to develop some novel and accurate solutions for Gross–Pitaevskii (GP) equations. A quantum system of identical bosons is described using the Hartree–Fock approximation and pseudopotential interaction model by the Gross–Pitaevskii equation (GPE), named after Eugene P. Gross and Lev Petrovich Pitaevskii. Many solitary wave solutions are constructed in various forms based on the implementation of the Khater II method and the novel Kudryashov method. The gained solutions are numerically represented in various graph styles. The validity of the solutions is investigated by applying the septic-B-spline scheme based on calculating the requested conditions from the obtained computational solutions. To make our study more applicable, we study the stability of our solutions by focusing on the Hamiltonian system’s properties. Mathematica 13.1 checks all inputs and outcomes against the original model for further confidence.

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.

Diverse novel analytical and semi-analytical wave solutions of the generalized (2+1)-dimensional shallow water waves model

Abstract: This article studies the generalized (2 + 1)-dimensional shallow water equation by applying two recent analytical schemes (the extended simplest equation method and the modified Kudryashov method) for constructing abundant novel solitary wave solutions. These solutions describe the bidirectional propagating water wave surface. Some obtained solutions are sketched in two- and three-dimensional and contour plots for demonstrating the dynamical behavior of these waves along shallow water. The accuracy of the obtained solutions and employed analytical schemes is investigated using the evaluated solutions to calculate the initial condition, and then the well-known variational iterational (VI) method is applied. The VI method is one of the most accurate semi-analytical solutions, and it can be applied for high derivative order. The used schemes’ performance shows their effectiveness and power and their ability to handle many nonlinear evolution equations.

Abundant closed-form solutions and solitonic structures to an integrable fifth-order generalized nonlinear evolution equation in plasma physics

Abstract: This paper investigates the evolution dynamics of closed-form solutions for a new integrable nonlinear fifth-order equation with spatial and temporal dispersion which describes shallow water waves moving in two directions. Some novel computational soliton solutions are obtained in the form of exponential rational functions, trigonometric and hyperbolic functions, and complex-soliton solutions. Some dynamical wave structures of soliton solutions are achieved in evolutionary dynamical structures of multi-wave solitons, double-solitons, triple-solitons, multiple solitons, breather-type solitons, Lump-type solitons, singular solitons, and Kink-wave solitons using the generalized exponential rational function (GERF) technique. All newly established solutions are verified by back substituting into the considered fifth-order nonlinear evolution equation using computerized symbolic computational work via Wolfram Mathematica. These newly formed results demonstrate that the considered fifth-order equation theoretically possesses very rich computational wave structures of closed-form solutions, which are also useful in obtaining a better understanding of the internal mechanism of other complex nonlinear physical models arising in the field of plasma physics and nonlinear sciences. The physical characteristics of some constructed solutions are also graphically displayed via three-dimensional plots by selecting the best appropriate constant parameter values to easily understand the complex physical phenomena of the nonlinear equations. Eventually, the results validate the effectiveness and trustworthiness of the used technique.

A New Perspective on the study of the fractal coupled Boussinesq-Burger equation in shallow water

Abstract: The well-known coupled Boussinesq–Burger equation can be used to describe the flow of the shallow water of the harbor. But when the boundary is nonsmooth, it becomes powerless. So, the fractal calc...