Search Results (420)

The (3 + 1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff equation, a model that describes long-wave interactions and has numerous applications in mathematics, engineering, and physics, is examined in this work. First, a wave transformation is used to reduce the equation to lower dimensions. The modified Khater method is then used to derive different types of solitary wave solutions, such as chirped, kink, periodic, and kink-bright types. By allocating suitable constant parameters, 3D, 2D, and contour plots are created to demonstrate the physical behavior of these solutions. Phase portraits are used to qualitatively analyze the undisturbed planar system using bifurcation theory. The system is then perturbed by an external force, resulting in chaotic dynamics. Chaos in the system is confirmed using multiple diagnostic tools, including time series plots, Poincaré sections, chaotic attractors, return maps, bifurcation diagrams, power spectra, and Lyapunov exponents. The stability of the model is further investigated with varying initial conditions. A bidirectional scatter plot technique, which efficiently reveals overlapping regions using data point distributions, is presented for comparing solution behaviors. Overall, this work offers useful tools for advancing applied mathematics research as well as a deeper understanding of nonlinear wave dynamics. Full article

Analysis of nonlinear plasma waves, formulated and applied for ionospheric HF heating experiments, indicates that Langmuir/upper hybrid waves excited by parametric instabilities can evolve into traveling solitary waves accompanied by self-induced cavitons. To explore these cavitons, a digisonde operating in fast mode was utilized. Significant results were observed in ionograms recorded two minutes after the activation of the O-mode heater. These ionograms displayed two distinct bumps in the virtual height spread, located slightly below both the HF reflection height and the upper hybrid resonance height. It is notable that these heights are also slightly below the excitation regions where Langmuir/upper hybrid Parametric Decay Instabilities (PDIs) are typically generated by an O-mode HF heater. These observations correlate with the theory and provide valuable insights into the dynamics of nonlinear plasma waves and their interaction with the ionosphere during HF heating experiments. Full article

Kinetic Alfvén waves (KAWs) are investigated in an Oxygen–Hydrogen plasma with electrons following the behavior of $rq$-distribution in an upper ionosphere. We aim to study low-frequency and long wavelengths at 1700 kms in the upper ionosphere of Earth as detected by Freja satellite. The fluid model and reductive perturbation method are combined to obtain the evolutionary wave equations that can be used to describe both fractional and non-fractional KAWs in an Oxygen–Hydrogen ion plasma. This procedure is used to obtain the integer-order Korteweg–de Vries (KdV) equation and then analyze its solitary wave solution. In addition, this study is carried out to evaluate the fractional KdV (FKdV) equation using a new approach called the “Tantawy technique” in order to generate more stable and highly accurate approximations that will be utilized to accurately depict physical events. This investigation also helps locate the existence regions of the solitary waves (SWs), and in turn displays that the characteristics of KAWs are affected by a number of physical factors, such as the nonthermal parameters/spectral indices “r”, “q”, and obliqueness (characterized by $l_z$). Depending on the parameter governing the distribution, especially the nonthermality of inertialess electrons, the $rq$-distribution of electrons has a major impact on the properties of KAWs. Full article

We studied traveling-wave solutions of the Dullin–Gottwald–Holm (DGH) equation via a sub-ODE construction. Under explicit algebraic constraints, the approach yielded closed-form families—bell-shaped, hyperbolic ($\mathrm{sech}/\tanh$), Jacobi-elliptic function (JEF), Weierstrass-elliptic function (WEF), periodic, and rational—and classified their symmetry properties. Optical solitons (bright and dark) arose as limiting cases of the elliptic solutions. We specified the parameter regimes that produced each profile and illustrated representative solutions with 2D/3D plots to highlight symmetry. The results provide a unified, reproducible procedure for generating solitary and periodic DGH waves and expand the catalog of exact solutions for this model. Full article

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

Coastal boulder deposits (CBDs) are important geomorphic indicators of extreme wave activity, yet integrated morphometric and hydrodynamic analyses remain limited along the Moroccan Atlantic coast. This study characterizes the morphology, spatial distribution, and transport thresholds of supratidal boulders at Oued Cherrat and Mansouria, and quantifies the wave energy required for their mobilization. Between 2021 and 2025, 85 boulders were surveyed, supported by lithological analyses, GPS mapping, and pre-/post-storm photographic documentation. At Oued Cherrat, boulders ranged from 0.01 to 3.56 m³ (≤7.84 t), with solitary blocks located 30–94 m inland and larger imbricated clasts up to 150.5 m. At Mansouria, dimensions reached 22 × 20 × 3.5 m (>2032 t), positioned 5–140 m from the shoreline. Storms in January and March 2025 displaced boulders up to 4.5 m at Oued Cherrat (e.g., 6.39 t) and up to 3 m at Mansouria (e.g., 21.42 t), with new blocks deposited and megaboulders showing slight in situ rotations. Hydrodynamic modelling estimated sliding thresholds of 1.1–4.0 m/s at Oued Cherrat and 2.7–11.0 m/s at Mansouria, while rolling thresholds reached 18.23 m/s. These values confirm the dependence of transport on boulder mass, imbrications, and topography. The findings demonstrate that extreme storms can rapidly reorganize multi-tonne CBDs, while the largest megaboulders require rare, exceptionally high-energy events. Full article

The stability of rubble mound breakwaters is highly affected by extreme wave loading. While extensive research has been devoted to wave-induced scour and liquefaction around breakwaters, comprehensive stability evaluations of the rubble mound breakwater core remain limited. This study develops a numerical framework to investigate the stability of rubble mound breakwaters subjected to solitary wave loading. Wave motion is modeled using the Navier–Stokes equations, wave-induced pore pressure is computed based on Darcy’s law, and soil behavior is represented through the Mohr–Coulomb constitutive model. The numerical model is validated against experimental data. To assess structural stability, the strength reduction method is employed to calculate the Factor of Safety (FOS) during wave propagation, with the minimum FOS serving as the stability criterion. Furthermore, the influence of key parameters, including wave height, soil shear strength, wave–current interaction, berm dimensions, and slope gradient, on breakwater stability is systematically analyzed. Full article

The detection of internal solitary waves (ISWs) in the ocean using Synthetic Aperture Radar (SAR) images is important for the safety of marine engineering structures. Based on 4120 Sentinel SAR images obtained from 2014 to 2024, an ISW dataset covering the Andaman Sea (AS), the South China Sea (SCS), the Sulu Sea (SS), and the Celebes Sea (CS) is constructed, and a deep learning dataset containing 3495 detection samples and 2476 segmentation samples is also established. Based on the YOLOv8 lightweight model, combined with an anti-interference strategy, a multi-size block detection strategy, and a post-processing repair module, an ISW detection method is proposed. This method reduces the false detection rate by 44.20 percentage points in terms of anti-interference performance. In terms of repair performance, the repair rate reaches 85.2%, and the error connection rate is less than 3.1%. The detection results of applying this method to Sentinel images in multiple sea areas show that there are significant regional differences in ISW activities in different sea areas: in the AS, ISW activities peak in the dry season of March and are mainly concentrated in the eastern and southern regions; the western part of the SS and the southern part of the CS are also the core areas of ISW activities. From the perspective of temporal characteristics, the SS maintains a relatively high ISW activity level throughout the dry season, while the CS exhibits more complex seasonal dynamic features. The lightweight detection method proposed in this study has good applicability and can provide support for marine disaster prevention work. Full article

This study presents a qualitative analysis of the fractional coupled nonlinear Schrödinger equation (FCNSE) to obtain its complete set of solutions. An appropriate wave transformation is applied to reduce the FCNSE to a fourth-order dynamical system. Due to its non-Hamiltonian nature, this system poses significant analytical challenges. To overcome this complexity, the dynamical behavior is examined within a specific phase–space subspace, where the system simplifies to a two-dimensional, single-degree-of-freedom Hamiltonian system. The qualitative theory of planar dynamical systems is then employed to characterize the corresponding phase portraits. Bifurcation analysis identifies the physical parameter conditions that give rise to super-periodic, periodic, and solitary wave solutions. These solutions are derived analytically and illustrated graphically to highlight the influence of the fractional derivative order on their spatial and temporal evolution. Furthermore, when an external generalized periodic force is introduced, the model exhibits quasi-periodic behavior followed by chaotic dynamics. Both configurations are depicted through 3D and 2D phase portraits in addition to the time-series graphs. The presence of chaos is quantitatively verified by calculating the Lyapunov exponents. Numerical simulations demonstrate that the system’s behavior is highly sensitive to variations in the frequency and amplitude of the external force. Full article

This study examines the soliton dynamics in the time-fractional cubic–quintic nonlinear non-paraxial propagation model, applicable to optical signal processing, nonlinear optics, fiber-optic communication, and biomedical laser–tissue interactions. The fractional framework exhibits a wide range of nonlinear effects, such as self-phase modulation, wave mixing, and self-focusing, arising from the balance between cubic and quintic nonlinearities. By employing the Multivariate Generalized Exponential Rational Integral Function (MGERIF) method, we derive an extensive catalog of analytic solutions, multi-peakon structures, lump solitons, kinks, and bright and dark solitary waves, while periodic and singular solutions emerge as special cases. These outcomes are systematically constructed within a single framework and visualized through 2D, 3D, and contour plots under both anomalous and normal dispersion regimes. The analysis also addresses modulation instability (MI), interpreted as a sideband amplification of continuous-wave backgrounds that generates pulse trains and breather-type structures. Our results demonstrate that cubic–quintic contributions substantially affect MI gain spectrum, broadening instability bands and permitting MI beyond the anomalous-dispersion regime. These findings directly connect the obtained solution classes to experimentally observed routes for solitary wave shaping, pulse propagation, and instability and instability-driven waveform formation in optical communication devices, photonic platforms, and laser technologies. Full article

This paper presents a detailed study of the $(3+1)$-dimensional Zakharov–Kuznetsov–Burgers equation to investigate shock-wave phenomena in dusty plasmas with quantum effects. The model provides significant physical insight into nonlinear dispersive and dissipative structures arising in charged-dust–ion environments, corresponding to both laboratory and astrophysical plasmas. We then perform a qualitative, numerically assisted dynamical analysis using bifurcation diagrams, multistability checks, return maps, Poincaré sections, and phase portraits. For both the unperturbed and a perturbed system, we identify chaotic, quasi-periodic, and periodic regimes from these numerical diagnostics; accordingly, our dynamical conclusions are qualitative. We also examine frequency-response and time-delay sensitivity, providing a qualitative classification of nonlinear behavior across a broad parameter range. After establishing the global dynamical picture, traveling-wave solutions are obtained using the Paul–Painlevé approach. These solutions represent shock and solitary structures in the plasma system, thereby bridging the analytical and dynamical perspectives. The significance of this study lies in combining a detailed dynamical framework with exact traveling-wave solutions, allowing a deeper understanding of nonlinear shock dynamics in quantum dusty plasmas. These results not only advance theoretical plasma modeling but also hold potential applications in plasma-based devices, wave propagation in optical fibers, and astrophysical plasma environments. Full article

This paper systematically studies the exact analytical solutions of the (2+1)-dimensional generalized Burgers–Fisher (gBF) equation. Using the Lie symmetry analysis method, the infinitesimal generators of the equation are derived. Through symmetry reduction, the original (2+1)-dimensional partial differential equation (PDE) is reduced to a (1+1)-dimensional equation, which is further transformed into an ordinary differential equation (ODE) via the traveling wave transformation. On this basis, a series of exact traveling wave solutions are successfully obtained by applying the generalized Bernoulli equation method, including hyperbolic tangent-type kink solitary wave solutions and hyperbolic cotangent-type singular soliton solutions. The study also conducts a visual analysis of the solution characteristics through three-dimensional graphs and contour plots. In particular, this paper discusses the case where the parameter n takes general values, filling the research gap in the existing literature. Full article

This study conducts an in-depth analysis of the dynamical characteristics and solitary wave solutions of the integrable Zhanbota-IIA equation through the lens of planar dynamic system theory. This research applies Lie symmetry to convert nonlinear partial differential equations into ordinary differential equations, enabling the investigation of bifurcation, phase portraits, and dynamic behaviors within the framework of chaos theory. A variety of analytical instruments, such as chaotic attractors, return maps, recurrence plots, Lyapunov exponents, Poincaré maps, three-dimensional phase portraits, time analysis, and two-dimensional phase portraits, are utilized to scrutinize both perturbed and unperturbed systems. Furthermore, the study examines the power frequency response and the system’s sensitivity to temporal delays. A novel classification framework, predicated on Lyapunov exponents, systematically categorizes the system’s behavior across a spectrum of parameters and initial conditions, thereby elucidating aspects of multistability and sensitivity. The perturbed system exhibits chaotic and quasi-periodic dynamics. The research employs the maximum Lyapunov exponent portrait as a tool for assessing system stability and derives solitary wave solutions accompanied by illustrative visualization diagrams. The methodology presented herein possesses significant implications for applications in optical fibers and various other engineering disciplines. Full article

Background: Picky eating often persists from childhood into adolescence, yet its temporal relation to solitary dinners is unknown. We examined the bidirectional links between eating dinner alone and picky eating across three developmental stages in a nationwide Japanese cohort. Methods: A total of 1389 two-parent families from the Japanese Longitudinal Study of Children and Parents participated in the study (grades 4–6 in 2015; grades 7–9 in 2018; grades 10–12 in 2021). Eating dinner alone (four-point scale) was analyzed as a two-part variable (binary ever/never + continuous frequency); picky eating was ordinal (four categories). A Bayesian Random Intercept Cross-Lagged Panel Model (RI-CLPM) with a two-part specification for eating alone was used to assess cross-lagged, autoregressive, and covariate paths; covariates were gender, grade sequence, parental education, and household income. Results: A single cross-lagged path proved significant: adolescents who ate dinner alone at least once per week in junior high school showed higher-than-their-own-average picky eating in high school, and the reverse paths were non-significant. Picky eating and the binary indicator of eating alone exhibited moderate positive autoregression, whereas the continuous frequency of solitary dinners showed a negative carry-over from Wave 1 to Wave 4, consistent with regression-to-the-mean. Boys, students in higher grades, and adolescents from higher-income households were more prone to solitary dinners, whereas girls exhibited higher trait-like levels of picky eating; parental education showed no significant associations. Conclusions: Frequent solitary dinners in junior high school may set the stage for later elevations in picky eating, underscoring the preventive value of shared family meals before early adolescence. Full article