Search Results (144)

In this study, the extended (3 + 1)-dimensional Jimbo–Miwa equation, which has not been previously studied using Lie symmetry techniques, is the focus. We derive new symmetry reductions and exact invariant solutions, including lump and rogue wave structures. Additionally, precise solitary wave solutions of the extended (3 + 1)-dimensional Jimbo–Miwa equation using the multivariate generalized exponential rational integral function technique (MGERIF) are studied. The extended (3 + 1)-dimensional Jimbo–Miwa equation is crucial for studying nonlinear processes in optical communication, fluid dynamics, materials science, geophysics, and quantum mechanics. The multivariate generalized exponential rational integral function approach offers advantages in addressing challenges involving exponential, hyperbolic, and trigonometric functions formulated based on the generalized exponential rational function method. The solutions provided by MGERIF have numerous applications in various fields, including mathematical physics, condensed matter physics, nonlinear optics, plasma physics, and other nonlinear physical equations. The graphical features of the generated solutions are examined using 3D surface graphs and contour plots, with theoretical derivations. This visual technique enhances our understanding of the identified answers and facilitates a more profound discussion of their practical applications in real-world scenarios. We employ the MGERIF approach to develop a technique for addressing integrable systems, providing a valuable framework for examining nonlinear phenomena across various physical contexts. This study’s outcomes enhance both nonlinear dynamical processes and solitary wave theory. Full article

In this study, we explore the soliton solutions of the truncated M-fractional fifth-order Korteweg–de Vries (KdV) equation by applying the improved modified extended tanh function method (IMETM). Novel analytical solutions are obtained for the proposed system, such as brigh soliton, dark soliton, hyperbolic, exponential, Weierstrass, singular periodic, and Jacobi elliptic periodic solutions. To validate these results, we present detailed graphical representations of selected solutions, demonstrating both their mathematical structure and physical behavior. Furthermore, we conduct a comprehensive linear stability analysis to investigate the stability of these solutions. Our findings reveal that the fractional derivative significantly affects the amplitude, width, and velocity of the solitons, offering new insights into the control and manipulation of soliton dynamics in fractional systems. The novelty of this work lies in extending the IMETM approach to the truncated M-fractional fifth-order KdV equation for the first time, yielding a wide spectrum of exact analytical soliton solutions together with a rigorous stability analysis. This research contributes to the broader understanding of fractional differential equations and their applications in various scientific fields. Full article

To address the building settlement issues induced by an urban geological hazard in a northern city, this study utilizes settlement monitoring data from 16 high-rise buildings. The non-uniform temporal data were processed using the Akima interpolation method to construct a settlement prediction model based on a backpropagation (BP) neural network. The model’s predictive performance was validated against traditional approaches, including the hyperbolic and exponential curve methods, and was further employed to estimate the stabilization time of building settlements. Additionally, spatiotemporal characteristics of settlement behavior under the influence of geological hazards were investigated through a comparative analysis of deformation data across the building group. The results demonstrate that the BP neural network model achieves a 58.3% improvement in predictive accuracy compared to traditional empirical methods, effectively capturing the settlement evolution of buildings. The model also provides reliable predictions for the time required for buildings to reach a stable state. The temporal evolution of building settlement exhibits a distinct three-stage pattern: (1) an initial abrupt phase dominated by rapid water and soil loss; (2) a rapid settlement phase primarily driven by the consolidation of sandy and clayey soils; and (3) a slow consolidation phase governed by the prolonged consolidation of cohesive soils. Spatially, building deformations show significant regional heterogeneity, and the existence of potential finger-like preferential pathways for water and soil loss appears to exert a substantial influence on differential settlements. Full article

In this paper we propose a statistical model that combines both autoregressions and fractional differentiation in a unified treatment. However, instead of imposing that the roots are strictly on the unit circle, we also allow them to be within the unit circle. This permits a higher degree of flexibility in the specification of the model, with rates of dependence combining exponential with hyperbolic decays. Monte Carlo experiments and empirical applications to climatological and financial data show that the proposed approach performs well. Full article

One of the tasks of statistical analysis is related to the development of forecasts with different horizons. The results of modeling the development trend can also be used for prognostic purposes. At the same time, the assumption is made that during the forecast period, the phenomenon under study will exhibit the same patterns of development that it exhibited during the base period. Network multimedia is a unifying link in the parallel development of multimedia and communication technologies. The integrated interaction of technological solutions in the field of multimedia and computer networks is a condition for achieving a greater final application effect in the presentation of information. Experimental studies of modern network multimedia in operational conditions are important for revealing bottlenecks in their functioning. On this basis, recommendations can be made to improve performance indicators, such as performance, reliability, mode of service, etc. This publication is devoted to the experimental study of the trend and the possibility of predicting network multimedia with time series. The implemented algorithm for automated trend determination examines pre-set different trends–linear, quadratic, cubic, hyperbolic, fractional-rational, logarithmic, exponential, exponential, combined–and chooses the most effective of them. Full article

A neural model was developed to predict the distribution of ZnO nanoparticles obtained by electrochemical synthesis. It is a three-layer multilayer perceptron (MLP) artificial neural network (ANN) with five neurons in the input layer, eight neurons in the hidden layer, and one neuron in the output layer. This network has a hyperbolic tangent activation function for the neurons in the hidden layer and an exponential activation function for the neuron in the output layer. The input (independent) variables are particle size (nm), solvent type, and temperature (°C), and the output (dependent) variable is fraction share (%). The best neural model (ann08) has a root mean square error (RMSE) 0.84% for the training subset, 0.98% for the testing subset, and 1.27% for the validation subset. The RMSE values are therefore small, which enables practical use of the ANN model. Full article

This paper investigates the surrounding control problem of multiple unmanned surface vehicles (USVs) against false data injection (FDI) attacks and proposes a learning-based prescribed performance control (PPC) integrated with a dynamic event-triggering (DET) mechanism. First, a predefined-time observer (PTO) is designed to estimate the injected false data. Then, the constrained surrounding tracking error of multi-USVs is first formulated based on an exponential prescribed performance function. To facilitate the control law design, the constrained surrounding problem is transformed into an unconstrained space using a hyperbolic tangent function. Based on adaptive dynamic programming (ADP) and the DET mechanism, a prescribed performance time-varying surrounding control scheme is developed. Finally, the effectiveness and superiority of the proposed control strategy are demonstrated through rigorous theoretical analysis and simulation experiments, while Zeno behavior in the event-triggered mechanism is excluded. Full article

We propose a novel Bayesian wavelet regression approach using a three-component spike-and-slab prior for wavelet coefficients, combining a point mass at zero, a moment (MOM) prior, and an inverse moment (IMOM) prior. This flexible prior supports small and large coefficients differently, offering advantages for highly dispersed data where wavelet coefficients span multiple scales. The IMOM prior’s heavy tails capture large coefficients, while the MOM prior is better suited for smaller non-zero coefficients. Further, our method introduces innovative hyperparameter specifications for mixture probabilities and scale parameters, including generalized logit, hyperbolic secant, and generalized normal decay for probabilities, and double exponential decay for scaling. Hyperparameters are estimated via an empirical Bayes approach, enabling posterior inference tailored to the data. Extensive simulations demonstrate significant performance gains over two-component wavelet methods. Applications to electroencephalography and noisy audio data illustrate the method’s utility in capturing complex signal characteristics. We implement our method in an R package, NLPwavelet (≥1.1). Full article

The increasing incorporation of renewable energy into power grids has significantly reduced system inertia and damping, posing challenges to frequency stability and power quality. To address this issue, an adaptive virtual synchronous generator (VSG) control strategy is proposed, which dynamically adjusts virtual inertia and damping in response to real-time frequency variations. Virtual inertia is modulated by an exponential function according to the frequency variation rate, while damping is regulated via a hyperbolic tangent function, enabling minor support during small disturbances and robust compensation during severe events. Control parameters are optimized using an enhanced particle swarm optimization (PSO) algorithm based on a composite performance index that accounts for frequency deviation, overshoot, settling time, and power tracking error. Simulation results in MATLAB/Simulink under step changes, load fluctuations, and single-phase faults demonstrate that the proposed method reduces the frequency deviation by over 26.15% compared to fixed-parameter and threshold-based adaptive VSG methods, effectively suppresses power overshoot, and eliminates secondary oscillations. The proposed approach significantly enhances grid transient stability and demonstrates strong potential for application in power systems with high levels of renewable energy integration. Full article

Accurate settlement prediction for high-speed railway (HSR) soft foundations remains challenging due to the irregular and dynamic nature of real-world monitoring data, often represented as non-equidistant and non-stationary time series (NENSTS). Existing empirical models lack clear applicability criteria under such conditions, resulting in subjective model selection. This study introduces a Monte Carlo-based evaluation framework that integrates data-driven simulation with geotechnical principles, embedding the concept of symmetry across both modeling and assessment stages. Equivalent permeability coefficients (EPCs) are used to normalize soil consolidation behavior, enabling the generation of a large, statistically robust dataset. Four empirical settlement prediction models—Hyperbolic, Exponential, Asaoka, and Hoshino—are systematically analyzed for sensitivity to temporal features and resistance to stochastic noise. A symmetry-aware comprehensive evaluation index (CEI), constructed via a robust entropy weight method (REWM), balances multiple performance metrics to ensure objective comparison. Results reveal that while settlement behavior evolves asymmetrically with respect to EPCs over time, a symmetrical structure emerges in model suitability across distinct EPC intervals: the Asaoka method performs best under low-permeability conditions (EPC ≤ 0.03 m/d), Hoshino excels in intermediate ranges (0.03 < EPC ≤ 0.7 m/d), and the Exponential model dominates in highly permeable soils (EPC > 0.7 m/d). This framework not only quantifies model robustness under complex data conditions but also formalizes the notion of symmetrical applicability, offering a structured path toward intelligent, adaptive settlement prediction in HSR subgrade engineering. Full article

This manuscript aims to explore localized waves for the nonlinear partial differential equation referred to as the $(1+1)$-dimensional generalized Kundu–Eckhaus equation with an additional dispersion term that describes the propagation of the ultra-short femtosecond pulses in an optical fiber. This research delves deep into the characteristics, behaviors, and localized waves of the $(1+1)$-dimensional generalized Kundu–Eckhaus equation. We utilize the multivariate generalized exponential rational integral function method (MGERIFM) to derive localized waves, examining their properties, including propagation behaviors and interactions. Motivated by the generalized exponential rational integral function method, it proves to be a powerful tool for finding solutions involving the exponential, trigonometric, and hyperbolic functions. The solutions we found using the MGERIF method have important applications in different scientific domains, including nonlinear optics, plasma physics, fluid dynamics, mathematical physics, and condensed matter physics. We apply the three-dimensional (3D) and contour plots to illuminate the physical significance of the derived solution, exploring the various parameter choices. The proposed approaches are significant and applicable to various nonlinear evolutionary equations used to model nonlinear physical systems in the field of nonlinear sciences. Full article

This paper investigates an integrable spin system known as the Myrzakulov-XIII (M-XIII) equation through geometric and gauge-theoretic methods. The M-XIII equation, which describes dispersionless dynamics with curvature-induced interactions, is shown to admit a geometric interpretation via curve flows in three-dimensional space. We establish its gauge equivalence with the complex coupled dispersionless (CCD) system and construct the corresponding Lax pair. Using the Sym–Tafel formula, we derive exact soliton surfaces associated with the integrable evolution of curves and surfaces. A key focus is placed on the role of geometric and gauge symmetry in the integrability structure and solution construction. The main contributions of this work include: (i) a commutative diagram illustrating the connections between the M-XIII, CCD, and surface deformation models; (ii) the derivation of new exact solutions for a fractional extension of the M-XIII equation using the Kudryashov method; and (iii) the classification of these solutions into trigonometric, hyperbolic, and exponential types. These findings deepen the interplay between symmetry, geometry, and soliton theory in nonlinear spin systems. Full article

This work presents a comprehensive mathematical framework for symmetrized neural network operators operating under the paradigm of fractional calculus. By introducing a perturbed hyperbolic tangent activation, we construct a family of localized, symmetric, and positive kernel-like densities, which form the analytical backbone for three classes of multivariate operators: quasi-interpolation, Kantorovich-type, and quadrature-type. A central theoretical contribution is the derivation of the Voronovskaya–Santos–Sales Theorem, which extends classical asymptotic expansions to the fractional domain, providing rigorous error bounds and normalized remainder terms governed by Caputo derivatives. The operators exhibit key properties such as partition of unity, exponential decay, and scaling invariance, which are essential for stable and accurate approximations in high-dimensional settings and systems governed by nonlocal dynamics. The theoretical framework is thoroughly validated through applications in signal processing and fractional fluid dynamics, including the formulation of nonlocal viscous models and fractional Navier–Stokes equations with memory effects. Numerical experiments demonstrate a relative error reduction of up to 92.5% when compared to classical quasi-interpolation operators, with observed convergence rates reaching $\mathcal{O}\left(n^{-1.5}\right)$ under Caputo derivatives, using parameters $\lambda =3.5$, $q=1.8$, and $n=100$. This synergy between neural operator theory, asymptotic analysis, and fractional calculus not only advances the theoretical landscape of function approximation but also provides practical computational tools for addressing complex physical systems characterized by long-range interactions and anomalous diffusion. Full article

The objective of this work is to investigate the global existence, general decay and blow-up results for a class of p-Biharmonic-type hyperbolic equations with delay and acoustic boundary conditions. The global existence of solutions has been obtained by potential well theory and the general decay result of energy has been established, in which the exponential decay and polynomial decay are only special cases, by using the multiplier techniques combined with a nonlinear integral inequality given by Komornik. Finally, the blow-up of solutions is established with positive initial energy. To our knowledge, the global existence, general decay, and blow-up result of solutions to p-Biharmonic-type hyperbolic equations with delay and acoustic boundary conditions has not been studied. Full article

This review provides a comprehensive overview of the closed-form expressions developed for estimating the soil water retention curve (SWRC) from 1964 to the present. Since the concept of the SWRC was introduced in 1907, numerous closed-form functions have been proposed to describe the relationship between soil matric suction and volumetric water content, each with distinct strengths and limitations. Given the variability in SWRC shapes influenced by soil texture, structure, and organic matter, models in the form of sigmoidal, multi-exponential, lognormal, hyperbolic, and hybrid functions have been designed to fit experimental SWRC data. Based on the number of adjustable parameters, these models are categorized into three main groups: three-, four-, and five-parameter models. They can also be classified as one-, two-, or three-segment functions depending on their structural complexity. A review of the developed models indicates that most are effective in representing the SWRC between the residual and saturated water content range. To capture the full range of the SWRC, hybrid functions have been proposed by combining traditional models. This review presents and discusses these models in chronological order of publication. Full article