Search Results (457)

Sea surface height anomaly (SSHA) observations from Surface Water and Ocean Topography (SWOT) provide a new opportunity for identifying crest lines of internal solitary waves (ISWs). However, L3 LR Unsmoothed SSHA is often affected by residual large-scale trends, rainfall contamination, and stripe noise, which limit segmentation performance. To address this issue, we propose an automatic segmentation workflow for SWOT SSHA. The workflow first applies Gaussian low-pass filtering for scale separation to extract high-frequency SSHA, then uses Otsu adaptive thresholding to segment ISW signals, and finally removes false targets using morphological geometric constraints. Validation based on 230 SWOT images from the northern South China Sea shows that, compared with the conventional method based on subtracting reanalysis fields, the proposed method increases the contrast-to-noise ratio (CNR) of high-frequency SSHA by 1.35 on average (Std = 0.99) and improves signal gain by 13.65 dB on average (Std = 7.71 dB). The method remains robust under complex conditions, including strong typhoons, severe stripe noise, weak shelf signals, and multi-wave interference. In some cases, quasi-synchronous optical imagery further confirms the authenticity of the extracted crest lines. Full article

The (2+1)-D generalized B-type Kadomtsev–Petviashvili (BKP) equation is studied in this work utilizing Painlevé property, Lie-symmetry method and generalized Kudryashov method (GKM). This study aims to pass the Painlevé test and obtain variant exact solutions for the (2+1)-D BKP equation that occurs in physical dynamics. First, we demonstrated that the governing equation exceeds the Painlevé test by using the Painlevé property. Symmetry analysis is utilized to obtain infinitesimals and vector fields of the BKP equation. The governing equation was converted to several ordinary differential equations (ODEs) using linear combinations of these vectors. GKM is used to generate a novel class of closed-form solutions for the BKP equation. Many random constants and functions were included in the derived solutions to improve their dynamic characteristics. The emergence of solutions was facilitated by the optimal selection of estimates for these elective constants. There are several types of solution behavior, such as a kink wave, solitary wave, anti-kink wave, and single wave. Full article

A recently proposed tensor–scalar extension of gravity coupled to extended Aharonov–Bohm electrodynamics admits one-variable traveling reductions in which a longitudinal electromagnetic scalar mode $S={\partial }_{\mu }{A}^{\mu }$ couples nonlinearly to gravitational scalars. In the weak-field regime outside sources, a one-dimensional traveling ansatz depending on $\xi =x-vt$ reduces the field equations to a coupled autonomous ODE system. The mathematical core of the reduction is a singular Newton-type equation whose classical mechanics counterpart is known; the novelty here lies in its derivation from the scalar–tensor/Aharonov–Bohm field system, in the physically motivated normalization of the traveling-wave families, and in the resulting phase–space interpretation for source-generated pulse selection. We provide a systematic classification of all admissible initial data and of the corresponding maximal solutions, distinguishing repulsive/attractive regimes and subcritical/critical/supercritical behaviors through a normalized parameter map. In particular, attractive branches may reach the singularity in finite time with a universal collision exponent $2/3$, while escaping branches exhibit asymptotically uniform motion with a computable logarithmic correction. Finally, we construct a numerical atlas of representative trajectories and validate the computations by cross-checking direct time integration against numerical inversion of the implicit quadrature, together with energy-defect diagnostics. Full article

With the large-scale construction of coastal high-speed railways, understanding the mechanical behavior of high-speed railway box girders under tsunami waves has become increasingly important. Existing studies on tsunami-induced forces on bridge girders have mainly focused on T-girders and plate-girders in highway bridges. In contrast, research on high-speed railway box girders, which are characterized by a significant height-to-width ratio, large cantilevers, and complex ancillary facilities on the girder top, remains relatively scarce, especially regarding its behavior under tsunami waves and the effects of lateral displacement on its dynamic response. In light of this, this study focuses on the investigation of the mechanical behavior of a single-track high-speed railway box girder under tsunami waves, and fifth-order solitary waves and dam-break waves are comparatively employed to simulate the typical unbroken and broken tsunami waves. The interaction between tsunami waves and the fixed railway box girder is numerically conducted, and the characteristics of the interaction process and the variation in maximum forces with girder clearance are thoroughly investigated. After that, the numerical interaction between tsunami waves and the laterally movable railway box girder is comparatively carried out, and the lateral displacement effects on the girder wave forces are exhaustively investigated. The results indicate that unbroken and broken tsunami waves exhibit distinctly different interaction processes with the box girder. With decreasing girder clearance, for the unbroken wave, the maximum horizontal and vertical forces occur when the girder bottom and the cantilever root descend to the initial water surface, respectively; for the broken wave, the horizontal and vertical forces simultaneously occur when the girder bottom nears the water surface with a small clearance. Lateral displacement can reduce wave forces on the girder, but the reduction is quite limited—remaining below 10% at the reference stiffness of an actual bearing. It validates that using a fixed girder model to estimate wave forces on an actual laterally movable girder is a slightly conservative and reasonable approach. This study provides further insight into wave forces acting on coastal high-speed railway box girders in tsunami-prone areas. Full article

Although extensive research has been carried out on the load characteristics of fixed submarines in internal solitary waves, there is still insufficient understanding of the effect of submarine speed on its motion in internal solitary waves. A rapid calculation method for the motion response of a submarine (SUBOFF standard model) in internal solitary waves between two layers of fluid is established in this study, where the internal wave flow field is constructed based on the extended Korteweg-de Vries theory, and the load on the submarine is calculated using the Morison equation. The accuracy of the proposed method is verified by comparison with numerical results and experimental data. The results of the motion response of the submarine when encountering internal solitary waves at different speeds show that there is a significant nonlinear relationship between speed and vertical motion amplitude and maximum pitch angle. A critical speed is further found, beyond which the submarine experiences a secondary falling deep after the initial vertical falling deep. Full article

Time-series machine learning models represented by long short-term memory (LSTM) networks provide an effective way to obtain high-precision sound speed profiles (SSPs) quickly and at low cost, which can meet the practical application requirements of underwater sonar systems. However, in sea areas with frequent strong internal solitary waves, the large-amplitude sound speed anomalies caused by them will seriously interfere with model learning in the form of strong outlier features, resulting in a sharp drop in SSP prediction accuracy and significant degradation of the generalization stability and robustness of the model. To address this problem, this paper proposes a time-series SSP prediction method based on a bidirectional long short-term memory (Bi-LSTM) network. First, Empirical Orthogonal Function (EOF) decomposition is used to realize the low-dimensional feature representation of SSPs, and then the bidirectional time-series feature capture capability of Bi-LSTM is used to predict the SSP sequence with large disturbances caused by strong internal solitary waves. Multiple groups of comparative experiments based on the measured temperature chain data in the continental slope area of the South China Sea show that the Bi-LSTM model has a significant improvement in prediction accuracy and robustness compared with the classical LSTM model. Among them, the Bi-LSTM model with EOF decomposition achieves a correlation coefficient of 0.995 and an average Root Mean Square Error (RMSE) as low as 0.387 m/s. Under the condition of internal solitary wave disturbance, the classical LSTM is difficult to effectively capture the large abrupt change in sound speed, while the proposed Bi-LSTM model can still achieve accurate prediction of the SSP in the disturbance section, and has both the feature recognition and evolution prediction capabilities for the strongly nonlinear internal solitary wave process. This method provides effective technical support for the rapid and large-scale reconstruction of the sound speed field under the disturbance of strong internal solitary waves. Full article

This paper examines the sixth-order generalized Boussinesq equation, which describes the dynamics of shallow-water waves, including the effects of surface tension. The study introduces Kudryashov’s R-function neural network approach for the first time, aiming to provide exact solutions to the nonlinear differential equation that represents the mathematical model of the sixth-order generalized Boussinesq equation. This technique incorporates the solutions of a nonlinear differential equation into neural networks, using them as an activation function within the hidden layer. In line with previous research on this topic, two categories of solutions are derived: solitary wave and shock wave solutions. Additionally, this paper includes 3D and 2D graphs to visually represent the solutions obtained. Full article

The analytically integrable Fokas system, arising under the slowly varying envelope approximation for weakly nonlinear and weakly dispersive quasi-monochromatic waves, is used to describe pulse propagation in single-mode optical fibers and is investigated here through symbolic computational techniques. This paper establishes multiple families of exact wave solutions through the combined use of the modified simple equation strategy and the generalized exponential rational function technique. These analytical approaches enable the derivation of diverse solitary and periodic wave structures characterized by adjustable parameters that control the amplitude, shape, and propagation dynamics of the waveform. To demonstrate the physical significance of the derived solutions, comprehensive graphical visualizations are provided, highlighting symmetric propagation features and diverse parameter-dependent behaviors of the wave structures. The flexibility of the obtained solution structures allows for a detailed examination of parameter-dependent wave dynamics and waveform evolution within the considered model. Moreover, a detailed modulation instability analysis is carried out to investigate the stability characteristics of continuous-wave solutions in the context of the Fokas system. The results identify parameter regimes associated with stable and unstable wave propagation, thereby enhancing the understanding of nonlinear instability phenomena in integrable optical models. In general, the study contributes new analytical wave structures, stability interpretations, and parametric insights that extend the applicability of the Fokas system in nonlinear wave theory and optical physics. Full article

In this study, we consider an extended form of the Kadomtsev–Petviashvili–Boussinesq equation motivated by wave propagation phenomena in dissipative media. The primary aim of this work is to construct exact analytical solutions and clarify the types of nonlinear wave structure admitted by the considered model. For this purpose, the Riccati equation expansion method is applied for the first time within this framework. This method allows us to obtain several distinct families of solitary wave solutions whose qualitative behaviors and physical characteristics are illustrated through graphical representations. In addition, modulation instability analysis is carried out to assess the stability of continuous wave solutions and further elucidate the underlying nonlinear dynamics of the system. Full article

Scholars are widely concerned about the research of nonlinear Rossby waves due to their essential importance in understanding the geophysical fluid dynamics. The effects of different topographies on the propagation of barotropic Rossby waves are discussed in this paper. Starting from the classical shallow water equation of uniformly rotating fluid with bottom topography, a new Schrödinger model equation of nonlinear Rossby wave amplitude is obtained by multi-scale spatial-temporal transformations and perturbation expansion method, which has an advantage in characterizing the propagation of the blocking for atmospheres. The evolutionary dynamics of dipole blocking are discussed analytically and are simulated numerically via changing terrain parameters for sinusoidal topography, slope topography, and roughed topography, respectively. The results show that the amplitude increase for sinusoidal bottom topography makes the dipole blocking move faster and enhances the intensity significantly. For sloped topography, the intensity of dipole blocking slowly decreases with increasing topographic slope. At the same time, the effect of the frequency for roughed topography agrees with the slope effect on the dynamics of nonlinear envelope solitary Rossby waves. This theoretical attempt gives a new explanation of the topographic Rossby waves. Full article

In this investigation, the nonlinear dust-acoustic waves in the lunar terminator region are studied in a three-component complex plasma comprising Boltzmann-distributed electrons and ions and inertial, cold, negatively charged dust grains. The fluid model is reduced, via the reductive perturbation technique, to a planar Korteweg–de Vries (KdV) equation that governs the evolution of small-amplitude dust-acoustic structures in this environment. Hirota’s direct method is then employed to derive exact multiple-soliton solutions, which allow us to examine the parameter dependence of dust-acoustic solitons and to characterize their overtaking collisions. The analysis shows that the soliton polarity and amplitude are controlled by the equilibrium electron–ion density ratio and the electron-to-ion temperature ratio, and that multi-soliton interactions remain elastic, with only finite phase shifts after collision. In the second part of the study, the planar integer KdV model is generalized to a time-fractional KdV (FKdV) equation to incorporate nonlocal temporal memory effects in the dust-acoustic dynamics. This FKdV equation is analyzed using two analytical approximation schemes: the Tantawy technique, recently proposed as a direct and rapidly convergent approach to fractional evolution equations, and the new iterative method, a widely used high-accuracy scheme in the fractional literature. For both methods, higher-order approximations are constructed, and their absolute and global maximum residual errors are quantified. The results demonstrate that the Tantawy technique provides compact approximations with superior accuracy and stability compared with the new iterative method for the present FKdV-soliton problem. The combined integer- and fractional-analytic framework provides a physically transparent framework for understanding how nonlinearity, dispersion, and fractional memory jointly shape dust-acoustic solitary structures in the electrostatically complex lunar terminator plasma, which is of paramount interest for future lunar missions like Luna-25 and Luna-27. Full article

The Korteweg–de Vries (KdV) equation is a foundational model in geophysical fluid dynamics (GFD), governing the propagation of long internal and surface gravity waves in stratified and shallow ocean environments where the interplay between nonlinear steepening and frequency-dependent dispersion gives rise to solitons. Although the analytical tractability of the KdV equation through inverse scattering is well established, systematic numerical exploration of multi-soliton interactions remains valuable for benchmarking solvers, probing conservation properties under varied oceanic initial conditions, and building intuition for more complex ocean wave phenomena. This article presents sangkuriang, an open-source Python library that solves the KdV equation using Fourier pseudo-spectral spatial discretization and adaptive eighth-order Runge–Kutta time integration. The implementation leverages just-in-time (JIT) compilation to achieve research-grade computational efficiency on standard hardware, making it readily accessible for coastal and ocean engineering applications, including idealized modeling of internal solitary waves on continental shelves, rapid parameter studies for solitary wave propagation in stratified basins, and pedagogical investigations of nonlinear dispersive wave dynamics. The solver is validated through four progressively complex idealized scenarios motivated by oceanic wave dynamics: isolated soliton propagation, symmetric interactions, overtaking collisions, and three-body interactions. High-fidelity conservation of mass, momentum, and energy is demonstrated, with relative errors remaining below $\mathcal{O}\left({10}^{-4}\right)$ across all test cases. Measured soliton velocities align with theoretical predictions within 5%, confirming the capture of the amplitude-dependent dispersion characteristic of oceanic solitary waves. Complementary diagnostics, including spectral entropy and recurrence quantification analysis (RQA), verify that the numerical solutions preserve the regular phase-space structure characteristic of integrable Hamiltonian systems. These results establish sangkuriang as a robust, lightweight platform for reproducible numerical investigation of idealized nonlinear dispersive wave dynamics relevant to coastal and ocean engineering applications. Full article

The present work is devoted to the analysis of a time-fractional Gardner equation arising in the modeling of nonlinear plasma waves in media endowed with memory and anomalous transport effects. Building on a physically motivated soliton profile, we construct a finite-time fractional ansatz in which the integer-order time variable is replaced by a fractional reparametrization that encodes the Caputo memory kernel. Within this framework, the governing evolution equation is not treated via a formal infinite expansion but rather via a finite approximation, whose quality is assessed directly via the associated residual. The Caputo fractional derivative is evaluated by a strong finite-difference formula that is second-order accurate in time and preserves the nonlocal convolution structure of the fractional operator. This combination of a finite fractional ansatz and a strong Caputo discretization allows us to compute the residual of the time analytically fractional Gardner equation and to use it as a quantitative diagnostic of accuracy and consistency. Two representative classes of nonlinear structures supported by the Gardner equation are examined in detail: a smooth solitary-wave profile and a cnoidal-wave configuration. For each example, the approximate fractional solution is generated, the corresponding residual is evaluated in space–time, and global and final-time residual norms are determined to quantify the influence of the fractional order on the wave dynamics and on the quality of the approximation. The numerical results show that the proposed residual-controlled approach yields residual magnitudes that remain one to two orders of magnitude smaller than those associated with truncated residual power-series approximations constructed from the same data, while preserving the expected qualitative features of fractional solitary and cnoidal waves in non-Markovian plasma environments. Full article

Background/Objectives: To evaluate whether adjunctive silodosin improves the stone-free rate (SFR) and clinical outcomes of extracorporeal shock wave lithotripsy (ESWL) for renal calculi. Methods: In this prospective randomised controlled trial, 100 adults with solitary radiopaque non-lower pole renal stones measuring 5–20 mm underwent single-session ESWL and were randomised (1:1) to receive either silodosin 8 mg once daily plus standard care or standard care alone for up to 12 weeks. Participants were followed up for three months. The primary outcome was SFR at three months on follow-up imaging. The secondary outcomes included time to stone clearance, renal colic episodes, analgesic requirement and adverse events. Results: At three months, the SFR was higher in the silodosin group than in the control group (68.0% vs. 50.0%; RR 1.36, 95% CI 0.97–1.90), but this difference did not reach statistical significance (p = 0.067). In a prespecified exploratory subgroup analysis, patients with stones measuring 10–20 mm showed a higher SFR with silodosin than controls (61.8% vs. 34.4%; p = 0.026), whereas no benefit was observed for stones measuring 5–9 mm (p = 0.803). Time-to-clearance analysis using Kaplan–Meier methods suggested earlier confirmed stone clearance in the silodosin group (hazard ratio 1.58, 95% CI 1.02–2.45; log-rank p = 0.036). Silodosin was also associated with fewer renal colic episodes and lower analgesic requirements. No serious drug-related adverse events were observed. Conclusions: This randomised controlled trial did not meet its primary endpoint because adjunctive silodosin did not significantly improve the overall SFR after ESWL. However, a possible benefit was observed in patients with renal stones measuring 10–20 mm, together with improved pain-related outcomes. These findings suggest that silodosin may have a role in selected patients, but the subgroup effects should be considered hypothesis-generating rather than definitive. Full article

The full symmetry group is found for a system of nonlinear schrödinger equations describing the propagation of optical pulses in an isotropic media. It is shown, in particular, that the six-dimensional symmetry group found is composed of a scaling transformation and a rotation of the four-dimensional space, thereby proving that the symmetry group preserves the shape of solutions. A symmetry classification of one-dimensional subalgebras of the Lie algebra is performed and yields, in particular, the symmetry reduction to the most general system of equations satisfied by the solitary waves of the equation. Explicit soliton solutions of the equation are found by largely autonomous technics. The found solitons are used to recursively generate two new ones by means of two iterations using the symmetry group. Other properties of the system are also highlighted, as well as the possible connections between the theories of symmetry groups and Darboux transformations inspired by this study. Full article