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The purpose of this paper is to study stability analysis, solition solutions and Gaussian solitons of the generalized nonlinear Schrödinger equation with higher order terms, which can be used to describe the propagation properties of optical soliton solutions.

The authors apply the ansatz method and the Hamiltonian system technique to find its bright, dark and Gaussian wave solitons and analyze its modulation instability analysis and stability analysis solution.

The results imply that the generalized nonlinear Schrödinger equation has bright, dark and Gaussian wave solitons. Meanwhile, the authors provide the graphical analysis of such solutions to better understand their dynamical behavior. Some constraint conditions are provided which can guarantee the existence of solitons. The authors analyze its modulation instability analysis and stability analysis solution.

These results may help us to further study the local structure and the interaction of solutions in generalized nonlinear Schrödinger -type equations. The authors hope that the results provided in this work can help enrich the dynamic behavior of the generalized nonlinear Schrödinger--type equations.

The purpose of this paper is to concern with a reliable treatment of the (2+1)-dimensional and the (3+1)-dimensional logarithmic Boussinesq equations (BEs). The author uses the sense of the Gaussian solitary waves to determine these gaussons. The study confirms that models characterized by logarithmic nonlinearity give gaussons solitons of distinct physical structures.

The proposed technique, as presented in this work has been shown to be very efficient for solving nonlinear equations with logarithmic nonlinearity.

The (2+1) and the (3+1)-dimensional BEs were examined as well. The examined models feature interesting results in propagation of waves and fluid flow.

The paper presents a new efficient algorithm for the higher dimensional logarithmic BEs.

The work shows the effect of logarithmic nonlinearity compared to other nonlinearities where standard solitons appear in the last case.

The work will benefit audience who are willing to examine the effect of logarithmic nonlinearity.

The paper presents a new efficient algorithm for the higher dimensional logarithmic BEs.

The purpose of this paper is to study the stability analysis and optical solitary wave solutions of a (2 + 1)-dimensional nonlinear Schrödinger equation, which are derived from a multicomponent plasma with nonextensive distribution.

Based on the ansatz and sub-equation theories, the authors use a direct method to find stability analysis and optical solitary wave solutions of the (2 + 1)-dimensional equation.

By considering the ansatz method, the authors successfully construct the bright and dark soliton solutions of the equation. The sub-equation method is also extended to find its complexitons solutions. Moreover, the explicit power series solution is also derived with its convergence analysis. Finally, the influences of each parameter on these solutions are discussed via graphical analysis.

The dynamics of these solutions are analyzed to enrich the diversity of the dynamics of high-dimensional nonlinear Schrödinger equation type nonlinear wave fields.

Aims to analyse unique deformation properties of textile materials in terms of basic mechanical properties. Models fabric deformation as a nonlinear dynamical system so that a fabric can be completely specified in terms of its mechanical behaviour under general boundary conditions. Fabric deformation is dynamically analogous to waves travelling in a fluid. A localized two‐dimensional deformation evolves through the fabric to form a three‐dimensional drape or fold configuration. The nonlinear differential equations arising in the analysis of fabric deformation belong to the Klein‐Gordon family of equations which becomes the sine‐Gordon equation in three dimensions. The sine‐Gordon equation has its origins in the study of Bäcklund Transformations in differential geometry. Describes fabric deformation as a series of transformations of surfaces, defined in terms of curvature parameters using Gaussian representation of surfaces. By considering a deformed fabric as a two‐dimensional surface, algebraically constructs analytical solutions of fabric deformation by solving the sine‐Gordon Equation. The theory of Bäcklund Transformations is used to transform a trivial solution into a series of solitary wave solutions. These analytical expressions describing the curvature parameters of a surface represent actual solutions of fabric dynamical systems.

The purpose of this paper is to find the exact solutions of a (3 + 1)-dimensional non-integrable Korteweg-de Vries type (KdV-type) equation, which can be used to describe the stability of soliton in a nonlinear media with weak dispersion.

The authors apply the extended Bell polynomial approach, Hirota’s bilinear method and the homoclinic test technique to find the rogue waves, homoclinic breather waves and soliton waves of the (3 + 1)-dimensional non-integrable KdV-type equation. The used approach formally derives the essential conditions for these solutions to exist.

The results show that the equation exists rogue waves, homoclinic breather waves and soliton waves. To better understand the dynamic behavior of these solutions, the authors analyze the propagation and interaction properties of the these solutions.

These results may help to investigate the local structure and the interaction of waves in KdV-type equations. It is hoped that the results can help enrich the dynamic behavior of such equations.

The purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.

This paper is based on the features of λ-tensor and the technique of six-dimensional formalism introduced by Pirani and followed by W. Borgiel, Z. Ahsan et al. and H.M. Manjunatha et al. This technique helps to describe both the geometric properties and the nature of the gravitational field of the space-times in the Segre characteristic.

The Gaussian curvature quantities specify the curvature of Bertotti–Kasner space-time. They are expressed in terms of invariants of the curvature tensor. The Petrov canonical form and the Weyl invariants have also been obtained.

The findings are revealed to be both physically and geometrically interesting for the description of the gravitational field of the cylindrical universe of Bertotti–Kasner type as far as the literature is concerned. Given the technique of six-dimensional formalism, the authors have defined the Weyl conformal λW-tensor and discussed the canonical form of the Weyl tensor and the Petrov scalars. To the best of the literature survey, this idea is found to be modern. The results deliver new insight into the geometry of the nonstatic cylindrical vacuum solution of Einstein's field equations.

The adoption of mobile payment remains low in certain regions, highlighting the need to identify the factors that enable and inhibit its adoption. This study aims to address this gap by investigating the role of information security, loss aversion and the moderating influence of the herd effect on Inertia and behavioral intentions in the adoption of mobile payment systems.

A structural equation model was developed and tested with 332 valid questionnaires to examine the proposed hypotheses.

The empirical results reveal that information security plays a significant role as an enabler, while loss aversion acts as an inhibitor of mobile payment adoption. Furthermore, the study uncovers the moderating influence of the herd effect on the relationship between Inertia and behavioral intentions.

This study was conducted in a specific region and may not be generalizable to other regions. Future studies could expand the sample size and scope to enhance the external validity of the findings.

This study offers practical implications for mobile payment service providers. Understanding the key enabling and inhibiting factors identified in this study can guide providers in designing and improving their services. Strengthening information security measures can help build trust among potential adopters, while offering incentives can mitigate the impact of loss aversion and encourage early adoption.

The findings of this study have social implications as they contribute to promoting the adoption of mobile payment systems. Increased adoption can enhance financial inclusion and stimulate economic development.

This study provides novel insights into the enabling and inhibiting factors of mobile payment adoption and highlights the moderating role of the herd effect. By shedding light on the influence of social norms on individual behavior in the context of mobile payment adoption, this study contributes to the existing literature and advances our understanding of this phenomenon.

The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.

An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.

The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.

The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.

The purpose of this paper is to both determine the effects of the nonlinearity on the wave dynamics and assess the temporal and spatial accuracy of five finite difference methods for the solution of the inviscid generalized regularized long-wave (GRLW) equation subject to initial Gaussian conditions.

Two implicit second- and fourth-order accurate finite difference methods and three Runge-Kutta procedures are introduced. The methods employ a new dependent variable which contains the wave amplitude and its second-order spatial derivative. Numerical experiments are reported for several temporal and spatial step sizes in order to assess their accuracy and the preservation of the first two invariants of the inviscid GRLW equation as functions of the spatial and temporal orders of accuracy, and thus determine the conditions under which grid-independent results are obtained.

It has been found that the steepening of the wave increase as the nonlinearity exponent is increased and that the accuracy of the fourth-order Runge-Kutta method is comparable to that of a second-order implicit procedure for time steps smaller than 100th, and that only the fourth-order compact method is almost grid-independent if the time step is on the order of 1,000th and more than 5,000 grid points are used, because of the initial steepening of the initial profile, wave breakup and solitary wave propagation.

This is the first study where an accuracy assessment of wave breakup of the inviscid GRLW equation subject to initial Gaussian conditions is reported.

The purpose of this paper is to develop a compressive sensing (CS) algorithm for noisy solder joint imagery compression and recovery. A fast gradient-based compressive sensing (FGbCS) approach is proposed based on the convex optimization. The proposed algorithm is able to improve performance in terms of peak signal noise ratio (PSNR) and computational cost.

Unlike traditional CS methods, the authors first transformed a noise solder joint image to a sparse signal by a discrete cosine transform (DCT), so that the reconstruction of noisy solder joint imagery is changed to a convex optimization problem. Then, a so-called gradient-based method is utilized for solving the problem. To improve the method efficiency, the authors assume the problem to be convex with the Lipschitz gradient through the replacement of an iteration parameter by the Lipschitz constant. Moreover, a FGbCS algorithm is proposed to recover the noisy solder joint imagery under different parameters.

Experiments reveal that the proposed algorithm can achieve better results on PNSR with fewer computational costs than classical algorithms like Orthogonal Matching Pursuit (OMP), Greedy Basis Pursuit (GBP), Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP) and Iterative Re-weighted Least Squares (IRLS). Convergence of the proposed algorithm is with a faster rate O(k*k) instead of O(1/k).

This paper provides a novel methodology for the CS of noisy solder joint imagery, and the proposed algorithm can also be used in other imagery compression and recovery.

According to the CS theory, a sparse or compressible signal can be represented by a fewer number of bases than those required by the Nyquist theorem. The new development might provide some fundamental guidelines for noisy imagery compression and recovering.