Search Results (272)

For a significant fluid model and the truncated M-fractional (1 + 1)-dimensional nonlinear generalized water wave equation, distinct types of truncated M-fractional wave solitons are obtained. Ocean waves, tidal waves, weather simulations, river and irrigation flows, tsunami predictions, and more are all explained by this model. We use the improved $(G^{\prime }/G)$ expansion technique and a modified extended direct algebraic technique to obtain these solutions. Results for trigonometry, hyperbolic, and rational functions are obtained. The impact of the fractional-order derivative is also covered. We use Mathematica software to verify our findings. Furthermore, we use contour graphs in two and three dimensions to illustrate some wave solitons that are obtained. The results obtained have applications in ocean engineering, fluid dynamics, and other fields. The stability analysis of the considered equation is also performed. Moreover, the stationary solutions of the concerning equation are studied through modulation instability. Furthermore, the used methods are useful for other nonlinear fractional partial differential equations in different areas of applied science and engineering. Full article

A comprehensive framework for ultrasound imaging simulations is presented. Solutions to an inhomogeneous wave equation are provided, yielding a linear model for characterizing ultrasound propagation and scattering in soft tissue. This simulation approach, which is based upon the fast nearfield method, is implemented in the Fast Object-oriented C++ Ultrasound Simulator (FOCUS) and is extended to a range of imaging modalities, including synthetic aperture, B-mode, plane wave, and color Doppler imaging. The generation of radiofrequency (RF) data and the receive beamforming techniques employed for each imaging modality, along with background on color Doppler imaging, are described. Simulation results demonstrate rapid convergence and lower error rates compared to conventional spatial impulse response methods and Field II, resulting in substantial reductions in computation time. Notably, the framework effectively simulates hundreds of thousands of scatterers without the need for a full three-dimensional (3D) grid, and the inherent randomness in the scatterer distributions produces realistic speckle patterns. A plane wave imaging example, for instance, achieves high fidelity using 100,000 scatterers with five steering angles, and the simulation is completed on a personal computer in a few minutes. Furthermore, by modeling scatterers as moving particles, the simulation framework captures dynamic flow conditions in vascular phantoms for color Doppler imaging. These advances establish FOCUS as a robust, versatile tool for the rapid prototyping, validation, and optimization of both established and novel ultrasound imaging techniques. Full article

The implementation of chaotic behavior and a sensitivity assessment of the newly developed M-fractional Kuralay-II equation are the foremost objectives of the present study. This equation has significant possibilities in control systems, electrical circuits, seismic wave propagation, economic dynamics, groundwater flow, image and signal denoising, complex biological systems, optical fibers, plasma physics, population dynamics, and modern technology. These applications demonstrate the versatility and advantageousness of the stated model for complex systems in various scientific and engineering disciplines. One more essential objective of the present research is to find closed-form wave solutions of the assumed equation based on the $({\displaystyle \frac{G^{\prime }}{G^{\prime }+G+A}})$-expansion approach. The results achieved are in exponential, rational, and trigonometric function forms. Our findings are more novel and also have an exclusive feature in comparison with the existing results. These discoveries substantially expand our understanding of nonlinear wave dynamics in various physical contexts in industry. By simply selecting suitable values of the parameters, three-dimensional (3D), contour, and two-dimensional (2D) illustrations are produced displaying the diagrammatic propagation of the constructed wave solutions that yield the singular periodic, anti-kink, kink, and singular kink-shape solitons. Future improvements to the model may also benefit from what has been obtained as well. The various assortments of solutions are provided by the described procedure. Finally, the framework proposed in this investigation addresses additional fractional nonlinear partial differential equations in mathematical physics and engineering with excellent reliability, quality of effectiveness, and ease of application. 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

Offshore cranes equipped with active motion compensation (AMC) systems play a vital role in marine engineering tasks such as offshore wind turbine maintenance, subsea operations, and dynamic load positioning under wave-induced disturbances. These systems rely on complex hydraulic actuators whose strongly nonlinear dynamics—often described by differential-algebraic equations (DAEs)—impose significant computational burdens, particularly in real-time applications like hardware-in-the-loop (HIL) simulation, digital twins, and model predictive control. To address this bottleneck, we propose a neural network-based surrogate model that approximates the actuator dynamics with high accuracy and low computational cost. By approximately reducing the original DAE model, we obtain a lower-dimensional ordinary differential equations (ODEs) representation, which serves as the foundation for training. The surrogate model includes three hidden layers, demonstrating strong fitting capabilities for the highly nonlinear characteristics of hydraulic systems. Bayesian regularization is adopted to train the surrogate model, effectively preventing overfitting. Simulation experiments verify that the surrogate model reduces the solving time by 95.33%, and the absolute pressure errors for chambers $p_1$ and $p_2$ are controlled within 0.1001 MPa and 0.0093 MPa, respectively. This efficient and scalable surrogate modeling framework possesses significant potential for integrating high-fidelity hydraulic actuator models into real-time digital and control systems for offshore applications. Full article

The primary aim of this research article is to investigate the soliton dynamics of the M-truncated derivative nonlinear Kodama equation, which is useful for optical solitons on nonlinear media, shallow water waves over complex media, nonlocal internal waves, and fractional viscoelastic wave propagation. We utilized two recently developed analytical techniques, the generalized Arnous method and the generalized Kudryashov method. First, the nonlinear Kodama equation is transformed into a nonlinear ordinary differential equation using the homogeneous balance principle and a traveling wave transformation. Next, various types of soliton solutions are constructed through the application of these effective methods. Finally, to visualize the behavior of the obtained solutions, three-dimensional, two-dimensional, and contour plots are generated using Maple (2023) mathematical software. Full article

This study explores analytical soliton solutions for the cubic–quintic time-fractional nonlinear non-paraxial pulse transmission model. This versatile model finds numerous uses in fiber optic communication, nonlinear optics, and optical signal processing. The strength of the quintic and cubic nonlinear components plays a crucial role in nonlinear processes, such as self-phase modulation, self-focusing, and wave combining. The fractional nonlinear Schrödinger equation (FNLSE) facilitates precise control over the dynamic properties of optical solitons. Exact and methodical solutions include those involving trigonometric functions, Jacobian elliptical functions (JEFs), and the transformation of JEFs into solitary wave (SW) solutions. This study reveals that various soliton solutions, such as periodic, rational, kink, and SW solitons, are identified using the complete discrimination polynomial methods (CDSPM). The concepts of chaos and bifurcation serve as the framework for investigating the system qualitatively. We explore various techniques for detecting chaos, including three-dimensional and two-dimensional graphs, time-series analysis, and Poincarè maps. A sensitivity analysis is performed utilizing a variety of initial conditions. Full article

This work explores the density-driven overturning circulation of the ocean using a process-oriented three-dimensional hydrodynamic model with a free sea surface. As expected, dense-water formation in polar regions creates a deep western boundary current (DWBC) spreading southward along the continental slope. Near the equator, the DWBC releases its water eastward into the ambient ocean to form a large upwelling zone. This upwelling is coupled with a slow westward surface recirculation feeding into a swift surface return flow along the western boundary that closes the mass budget. This recirculation pattern, which is fundamentally different to the Stommel–Arons model, is a consequence of geostrophic adjustment to anomalies of the surface pressure field that form under the influence of both coastal and equatorial Kelvin waves and Rossby waves. Based on the findings, the author presents a revised model of the ocean’s meridional overturning circulation to supersede earlier, incorrect suggestions. Full article

This study proposes a three-dimensional numerical wave tank (NWT) to calculate wave propagation and hydrodynamic forces based on the Navier–Stokes equation, using commercial Computational Fluid Dynamic (CFD) software ANSYS Fluent. The VOF Method is utilized to identify the free surface. The CFD model employed for generating waves in the NWT is initially verified using analytical theory to evaluate the accuracy of the results. In addition, the User-Defined Function (UDF) in ANSYS Fluent is implemented to ensure the model performs under the oscillatory conditions of the Submerged Horizontal Plate (SHP) Wave Energy Converter (WEC) device, which is localized at the center of the NWT. Finally, the influence of SHP oscillation on the device’s average efficiency was analyzed by comparing seven cases with different geometric configurations, considering both the oscillating and non-oscillating conditions of the SHP under the incidence of different waves. The results indicated that the geometric configuration and wave conditions of Case 4 achieved the best performance, reaching an average efficiency of 35.68%. Full article

The main purpose of this article is to study the optical solutions of the nonlinear Kodama equation with the M-truncated derivative by using the extended $(G^{\prime }/G)$-expansion method. Firstly, the nonlinear Kodama equation with the M-truncated derivative is transformed into a nonlinear ordinary differential equation based on the principle of homogeneous equilibrium and the traveling wave transformation. Secondly, the optical solutions of the nonlinear Kodama equation with the M-truncated derivative are constructed by using the extended $(G^{\prime }/G)$-expansion method. Finally, three-dimensional, two-dimensional, and contour maps of partial solutions are obtained by using Matlab R2023b mathematical software. Full article

In this article, novel methods of analysis to solve the (3+1)-dimensional generalized fractional Kadomtsev–Petviashvili equation, which plays a crucial role in the modelling of fluid dynamics, particularly wave propagation in complicated media, are presented. The fractional KP equation, a well-established mathematical model, uses fractional derivatives to more adequately describe more general types of nonlinear wave phenomena, with a richer and improved understanding of the dynamics of fluids with non-classical characteristics, such as anomalous diffusion or long-range interactions. Two efficient methods, the exponential rational function technique (ERFT) and the generalized Kudryashov technique (GKT), have been applied to find exact travelling solutions describing soliton behaviour. Solitons, localized waveforms that do not deform during propagation, are central to the dynamics of waves in fluid systems. The characteristics of the obtained results are explored in depth and presented both by three-dimensional plots and by two-dimensional contour plots. Plots provide an explicit picture of how the solitons evolve in space and time and provide insight into the underlying physical phenomena. We also added modulation instability. Our analysis of modulation instability further underscores the robustness and physical relevance of the obtained solutions, bridging theoretical advancements with observable phenomena. Full article

This article investigates the qualitative analysis and traveling wave solutions of a (3 + 1)-dimensional generalized nonlinear Konopelchenko-Dubrovsky-Kaup-Kupershmidt system. This equation is commonly used to simulate nonlinear wave problems in the fields of fluid mechanics, plasma physics, and nonlinear optics, as well as to transform nonlinear partial differential equations into nonlinear ordinary differential equations through wave transformations. Based on the analysis of planar dynamical systems, a nonlinear ordinary differential equation is transformed into a two-dimensional dynamical system, and the qualitative behavior of the two-dimensional dynamical system and its periodic disturbance system is studied. A two-dimensional phase portrait, three-dimensional phase portrait, sensitivity analysis diagrams, Poincaré section diagrams, and Lyapunov exponent diagrams are provided to illustrate the dynamic behavior of two-dimensional dynamical systems with disturbances. The traveling wave solution of a Konopelchenko-Dubrovsky-Kaup-Kupershmidt system is studied based on the complete discriminant system method, and its three-dimensional, two-dimensional graphs and contour plots are plotted. These works can provide a deeper understanding of the dynamic behavior of Konopelchenko-Dubrovsky-Kaup-Kupershmidt systems and the propagation process of waves. Full article

The generalized (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa (gDJKM) equation, which can be used to describe some phenomena in fluid mechanics, is investigated based on the multi-soliton solution. Soliton molecules of the gDJKM equation are given by the velocity resonance mechanism. A soliton molecule containing three solitons is portrayed at different times. The invariance of the relative positions of three solitons confirms that they form a soliton molecule. Multi-order lumps are obtained by applying the long-wave limit method in the multi-soliton. By analyzing the dynamics of one-order and two-order lumps, the energy concentration and localization property for lump waves are displayed. In the meanwhile, a multi-soliton can transform into multi-order breathers by the complex conjugation relations of parameters. The interaction among lumps, breathers and soliton molecules can be constructed by combining the above comprehensive analysis. The interaction between a one-order lump and a soliton molecule is an elastic collision, which can be observed through investigating evolutionary processes. The results obtained in this paper are useful for explaining certain nonlinear phenomena in fluid dynamics. Full article

The aim of this study is to examine the behavior of subharmonics in a one-dimensional cavity filled with a bubbly liquid, leveraging the nonlinear softening phenomenon of the medium at high amplitudes to enhance subharmonic generation. To this purpose, we use a numerical model developed previously that solves a coupled differential system formed by the wave equation and a Taylor-expanded Rayleigh–Plesset equation. This system describes the nonlinear mutual interaction between ultrasound and bubble vibrations. We carry out several different simulations to measure the response of the subharmonic component $f/2$ and the acoustic source frequency signal f when the cavity is excited over a range around the linear resonance frequency of the cavity (the resonance value obtained at low pressure amplitudes). Different source amplitudes in three different kinds of medium are used. Our results reveal several new characteristics of subharmonics as follows: their generation is predominant compared to the source frequency; their generation is affected by the softening of the bubbly medium when acoustic pressure amplitudes are raised; this specific behavior is solely an acoustically-related phenomenon; their behavior may indicate that the bubbly liquid medium is undergoing a softening process. Full article

Building vibration induced by running trains or other loads is related to soil vibration, building coupling loss, and the building floor’s amplification factor. In order to predict the vibration response of the proposed building caused by various loads, the propagation law of Rayleigh wave in saturated foundation soil and the refraction and transmission coefficients of Rayleigh wave between saturated soil and building structure are analyzed by using the theoretical analysis method, and the building coupling loss coefficient is obtained. The dynamic equation of the building’s structural vibration is established, and the analytical expression of the floor amplification factor is derived. A frame structure building is selected as the specific research object. Based on the Kirchhoff thin plate theory, the three-dimensional frame structure characteristic matrix of the building is obtained, and the vertical displacement values of each floor of the building under the action of the Ricker pulse load are calculated. The results are compared with the results in the literature, which verifies the effectiveness and accuracy of the transfer function method proposed in this study and fills the gap of insufficient research on the analysis of displacement transfer loss in soil structure interaction (SSI) in the literature. Full article