In this paper, we study a split-step Galerkin finite element (FE) method for the two-dimensional Riesz space-fractional coupled nonlinear Schrödinger equations (CNLSs). The proposed method adopts a second-order split-step technique to handle the...
This study focuses on analyzing the almost sure exponential stability of the split-step
This paper addresses a stochastic pantograph model with Lévy leaps where non-jump coefficients exceed linearity. The partially truncated split-step theta method is introduced and applied to the proposed model. The finite time
This paper studies the stochastic pantograph model, which is considered a subcategory of stochastic delay differential equations. A more general jump process, which is called the Lévy process, is added to the model for better performance and m...
This article proposes an advanced algorithm for the numerical solution of a coupled nonlinear Schrödinger equations system describing the evolution of a high-power femtosecond optical pulse in a single-mode polarization-maintaining optical fiber. We...
We introduce two approaches by modifying split-step exponential schemes to study stochastic differential equations. Under the Lipschitz condition and linear-growth bounds, it is shown that our explicit schemes converge to the solution of the correspo...
In this paper, the improved split-step
This research addresses and resolves current challenges in meshless Lagrangian methods for simulating viscoelastic materials. A split-step scheme, or pressure Poisson reformulation of the Navier–Stokes equations, is introduced for incompressibl...
This paper investigates the general decay stability of the stochastic linear theta (SLT) method and the split-step theta (SST) method for stochastic delay Hopfield neural networks. The definition of general decay stability for numerical solutions is...
In this paper, an SVIR epidemic model with temporary immunities and general incidence rates is constructed and analyzed. By utilizing Lyapunov functions, we prove the existence and uniqueness of the positive global solution of the constructed model,...
This paper presents a partially symmetric regularized two-step inertial alternating direction method of multipliers for solving non-convex split feasibility problems (SFP), which adds a two-step inertial effect to each subproblem and includes an inte...
In the context of improving the dimensioning of observation and telecommunication, the characterization of the propagation canal is very important. Thus, accurate models of propagation phenomenona in their environment and above a rough surface (marit...
Traditional femtosecond laser modeling relies on the iterative solution of the Nonlinear Schrödinger Equation (NLSE) using the Split-Step Fourier Method (SSFM). However, SSFM’s high computational complexity leads to significant time consum...
The propagation of femtosecond pulses in guided structures is a matter of both fundamental and practical interest in nonlinear optics. In particular, hollow-core waveguides (HCWs) filled with a gas medium are fabricated and used as devices for the ge...
We analytically and numerically investigate the stability and dynamics of the plane wave solutions of the fractional nonlinear Schrödinger (NLS) equation, where the long-range dispersion is described by the fractional Laplacian
Accurately predicting high-energy laser propagation toward fast-moving aerial targets is not straightforward, since the slant range, elevation angle, atmospheric path, accumulated turbulence, and thermal blooming all change along with target motion....
We present for the first time an approach about Bose–Einstein condensates made up of atoms with attractive interatomic interactions confined to the Pöschl–Teller hyperbolic potential. In this paper, we consider a Bose–Einstein...
Two 1D nonlinear coupled Schrödinger equations are often used for describing optical frequency conversion possessing a few conservation laws (invariants), for example, the energy’s invariant and the Hamiltonian. Their influence on the properties of t...
Applications and modeling of various phenomena in all areas of scientific research require finding numerical solutions for differential, partial differential, integral, or integro-differential equations. In addition to proving theoretical convergence...
We study the collision dynamics of two Bose–Einstein condensates, with their dynamical wave functions modeled by a set of coupled, time-dependent Gross–Pitaevskii equations. In an effective one-dimensional system, we identify regimes char...
The purpose of this work is to construct iterative methods for solving a split minimization problem using a self-adaptive step size, conjugate gradient direction, and inertia technique. We introduce and prove a strong convergence theorem in the frame...
The effects of doping manganese ions into a cerium oxide lattice for a thermochemical two-step water-splitting cycle to produce oxygen and hydrogen and new synthesis methods were experimentally investigated. In order to comparison of oxygen/hydrogen...
Background: This research investigates the biomechanical impact of the split-step technique on forehand and backhand lunges in badminton, aiming to enhance players’ on-court movement efficiency. Despite the importance of agile positioning in ba...
A two-step simplified modulus-based matrix splitting iteration method is presented for solving the linear complementarity problem. According to general matrix splitting and special matrix splitting, a general convergence analysis and a specific conve...
In this paper, we focus on studying the split feasibility problem (SFP) in Hilbert spaces. Based on the CQ algorithm involving the self-adaptive technique, we introduce a three-step iteration process for approximating the solution of SFP. Then, the c...
A modified viscosity-type self-adaptive iterative algorithm is presented in this study, having a strong convergence theorem for estimating the common solution to the split generalized equilibrium problem along with the split common null point problem...
We present a fully discrete splitting-Galerkin scheme for second-order, non-autonomous abstract Cauchy problems with time-dependent perturbations. By reformulating the second-order equation as a first-order system in the product space, we apply a Gal...
In this paper, two Halpern-type inertial iteration methods with self-adaptive step size are proposed for estimating the solution of split common null point problems (
In this paper, a two-step iteration method was established which can be viewed as a generalisation of the existing modulus-based methods for vertical linear complementarity problems. The convergence analysis of the proposed method is presented, which...
The construction of high-performance catalysts for overall water splitting (OWS) is crucial. Nickel–iron-layered double hydroxide (NiFe LDH) is a promising catalyst for OWS. However, the slow kinetics of the HER under alkaline conditions seriou...
This paper presents an open-source time-dependent three-dimensional scalar photorefractive beam propagation model (PRProp3D) based on the well-known split-step method. The angular spectrum method is used for the diffractive steps, and the nonlinearit...
In the synthesis method of a BiVO4 photoanode via BiOI flakes, a BiOI film is formed by electrochemical deposition in Step 1, and a vanadium (V) source solution is placed by drop-casting on the BiOI film in Step 2. Following this, BiVO4 particles are...
In this work, we develop a vectorial model, for optical communications, using distributed Raman amplification (DRA) applied to vectorial soliton pulses in monomode fiber optics. The main result, a dependent polarization effective Raman gain coefficie...
The propagation characteristics of a single Airy beam in nonlinear Kerr media were numerically investigated by utilizing the split-step Fourier transform method. We show that in addition to normal breathing solitons, the anomalous bound states of Air...
The results of a computer simulation of laser beams focused by a combined multichannel array system in the atmosphere are presented. Beam propagation on atmospheric paths is considered taking into account the influence of turbulence and time-dependen...
In this paper, we theoretically investigate the stability of spin-wave solitons in Bose-Einstein condensates of repulsive magnons, confined by an inhomogeneous external magnetic field described by a Gaussian well. For this purpose, we use the quasi-o...
We present a method to study the dynamics of a quasi-two dimensional Bose-Einstein condensate which initially contains several vortices at arbitrary locations. The method allows one to find the analytical solution for the dynamics of the Bose-Einstei...
The Airyprime beam, due to its adjustable focusing ability and controllable orbital angular momentum, has attracted significant attention in fields such as free-space optical communication and particle trapping. However, systematic studies on the pro...
This paper discusses novel approaches to the numerical integration of the coupled nonlinear Schrödinger equations system for few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In...
In fiber optic communication systems, the dispersion and nonlinear interaction of optical signals are critical to modeling fiber optic communication, and the regular perturbation (RP) model is a simplified modeling method composed of parallel branche...
Fiber amplifiers are essential devices for optical communication and laser physics, yet the intricate nonlinear dynamics they exhibit pose significant challenges for numerical modeling. In this study, we propose using a bi-LSTM neural network to pred...
Heating systems are essential municipal infrastructure in winter, especially in severe cold cities of China. The safety and efficiency of heating systems greatly affect building energy efficiency and indoor thermal comfort. Heating networks (HNs), pl...
Highly nonlinear suspended-core fibers (SCFs) with tunable dispersion have attracted much attention in the fields of Raman amplification, optical frequency combs, broadband and flat supercontinuum generation (SCG). To address the limitation of applic...
The supercontinuum generation and manipulation of Airy-Gaussian pulses in a photonic crystal fiber with three zero-dispersion points are studied using the split-step Fourier method. Firstly, the spectral evolution of Airy-Gaussian pulses in four phot...
In this paper, the (2+1)-dimensional nonlinear Schrödinger equation (2D NLSE) abreast of the (2+1)-dimensional linear time-dependent Schrödinger equation (2D TDSE) are thoroughly investigated. For the first time, these two notable 2D equati...
The last few years, many studies have been published on the 3rd-order inverse Volterra series transfer function nonlinear equalizer (IVSTF-NLE) in long-haul optical communication systems. Nonetheless, no experimental work has been published on invest...
This paper introduces a novel meshless and Lagrangian approach for simulating non-Newtonian flows, named Lagrangian Differencing Dynamics (LDD). Second-order-consistent spatial operators are used to directly discretize and solve generalized Navier–St...
Reliable estimation of radio wave propagation across irregular terrain is essential for the effective planning and optimization of contemporary wireless communication systems, such as cellular networks, broadcasting infrastructure, and radar systems....
We study a system of ultra-cold dipolar Bose gas atoms confined in a two-dimensional (2D) harmonic trap with a dipolar impurity implanted at the center of the trap. Due to recent experimental progress in dipolar condensates, we focused on calculating...
The maritime desert boundary layer over Bahrain often supports anomalous tropospheric propagation. This includes super-refraction and surface-based ducting. These conditions increase the risk of transboundary VHF interference across the Arabian Gulf....
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