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This study aims to apply two highly effective and precise analytical methods: the Aboodh residual power series method and the Aboodh transform iterative method. These enhanced techniques are utilised to analyse and solve two types of fractional physical evolutionary wave equations including the planar fractional Kawahara equation and the planar fifth-order Korteweg–de Vries (FKdV) equation. The mentioned approaches are a mixed form of the standard Aboodh transform with the standard residual power series method and iterative method. Some highly accurate analytical approximate solutions are derived using the two proposed approaches. In these techniques, the generated approximations are expressed as convergent series solutions. All generated approximations are analysed both graphically and numerically to gain insight into the dynamics of the nonlinear phenomena they represent, including planar solitary waves. The absolute error is also computed to assess the generated approximations’ precision and validate the efficacy of the proposed approaches. The fractional evolutionary wave equations (EWEs) under study are widely used to analyse and model various nonlinear structures that emerge and propagate in fluid mechanics, plasma physics and optical physics. Consequently, the derived approximations are expected to reveal some behaviours not shown by the exact solutions of these equations in their integer cases.

Our approach in the present work is concerned with a novel study involving a sampled-data controller for hybrid nanofluid in a time-delay nonlinear Brinkman system with randomly occurring uncertainties. The time-delay error system is described by utilising a hybrid nanofluid in nonlinear system and the looped Lyapunov–Krasovskii functional with a splitting sampling interval. In order to ensure that the resulting closed-loop system is reliable, it is asymptotically stable and has the required dissipative efficiency. A master/slave synchronisation technique is employed to synchronise the hybrid nanofluid in nonlinear system. In addition, we employed a sampling interval ([t_{k}, t_{k+1}]) and the fractional parameter ({tilde{beta }}) in the interval [0,1] has split into ([t_{k}, t_{k} +{tilde{beta }} varsigma _{1}(t)], [ t_{k} +{tilde{beta }} varsigma _{1}(t), t], [t, t +{tilde{beta }} varsigma _{2}(t)]) and ( [ t +{tilde{beta }} varsigma _{2}(t), t_{k+1}]). Then, the synchronised hybrid system utilises the looped Lyapunov stability theory and positive definite matrix. The simulation results not only confirm the theoretical predictions but also demonstrate enhanced control performance, improved synchronisation accuracy and robust dynamic stability. Furthermore, this study highlights the impact of time-delay, uncertainty and fractional parameter variations on system stability. The proposed approach provides a new direction for advanced control strategies in nanofluid-based nonlinear systems, offering potential applications in engineering and industrial processes. Finally, certain simulation results verify the effectiveness and correctness of the analytical results.

In recent years, nanoplastics have attracted increasing attention due to their widespread presence in the environment and potential harm to living organisms. To provide a theoretical basis for using surface-enhanced Raman spectroscopy (SERS) mechanism to detect nanoplastics of different sizes, this work employed lasers to irradiate the substrate composed of a bowl-shaped particle-in-cavity structure and nanoplastics. Then, the electric field distribution was obtained using the finite-difference time-domain (FDTD) method. By altering the curvature of the Ag nanobowl and the size of gold nanoparticles (AuNPs), the electric field enhancement capability of this SERS structure can be ameliorated. It is found that when the diameter of AuNPs is 30 nm, the larger the nanoplastics, the more suitable the structure with smaller curvature as a substrate. But when the diameter of AuNPs is 40 nm, the larger the nanoplastics, the more suitable the structure with larger curvature as a substrate. AuNPs with a size of 40 nm are generally superior to those with a size of 30 nm. To verify the feasibility of this SERS structure for detecting various nanoplastics, we tested a range of nanoplastic materials. The results prove that the materials of nanoplastics will not have a significant impact on the detection. Moreover, a multi-hot-spot system is analysed to reveal the SERS signal enhancement mechanism. A laser of 785 nm can produce stronger ‘localised hot spots’ (LHSs) and weaker ‘volume hot spots’ (VHSs) than a laser of 532 nm. The issue of nanoplastic detection is optimistically poised for resolution, as the hot spots within the bowl-shaped particle-in-cavity structure can effectively approach and surround nanoplastics, stimulating highly intense SERS signals that demonstrate their promising application in nanoplastic detection.

Bell–Kochen–Specker theorem states that a non-contextual hidden-variable theory cannot completely reproduce the predictions of quantum mechanics. Asher Peres gave a remarkably simple proof of quantum contextuality in a four-dimensional Hilbert space of two spin-1/2 particles. Peres’ argument is enormously simpler than that of Kochen and Specker. Peres contextuality demonstrates a logical contradiction between quantum mechanics and non-contextual hidden variable models by showing an inconsistency when assigning non-contextual definite values to a certain set of quantum observables. In this work, we present a similar proof in time with a temporal version of the Peres-like argument. In analogy with the two-particle version of Peres’ argument in the context of spin measurements at two different locations, we examine here single-particle spin measurements at two different times (t=t_1) and (t=t_2). We adopt three classical assumptions for time-separated measurements, which are demonstrated to conflict with quantum mechanical predictions. Consequently, we provide a non-probabilistic proof of certified quantumness in time, without relying on inequalities, demonstrating that our approach can certify the quantumness of a device through single-shot, time-separated measurements. Our results can be experimentally verified with the present quantum technology.

A five-level microwave-driven X-type scheme is used to study the influence of various field parameters on the absorption and nonlinear dispersion of probe light. In the proposed system, the cross-Kerr nonlinearity can be enhanced by optimum setting of the field strength and detunings. Our calculation reveals that the amplitude and position of the cross-Kerr peaks can be manipulated by tuning the microwave Rabi frequency and relative phase parameter. This proposed scheme has potential applications in the realm of multichannel quantum gates.

Photovoltaic materials are highly effective for solar cells, offering high efficiency and stability. Quantum theoretical analysis of phosphides [Sr₃Sn₂P₄]: Eu³⁺ for their potential in photovoltaic applications is reported here for the first time. Quantum computations for Sr₃Sn₂P₄ optoelectronics, mechanical and transport properties were performed using the all-electron method. The calculations were performed using the generalised gradient approximation plus Hubbard potential U (GGA + U) method for the doped materials. Our research indicates that the Sr₃Sn₂P₄ band gap can be lowered from 1.65 to 1.0 eV by doping Eu³⁺. According to first-principles calculations, bands at the Fermi level are hybridised with Sr-d, Sn-p and P-p orbitals. Eu³⁺ doping enables fine-tuning of the material’s band gap, structure and optoelectronic properties of novel phosphides by expanding the material’s potential applications in the semiconductor industry. Furthermore, calculations of the transport properties using semi-classical Boltzmann theory reveal a consistent pattern of thermopower throughout the 100–800 K range, which opens the door to the potential use of these compounds as low-temperature thermoelectric materials. ZT calculations show that both materials have reasonably strong thermoelectric performance, with just a slight fluctuation (0.18) in the results throughout a wide temperature range. Additionally, a thorough examination of the transport properties indicates that the current series of materials is p-type semiconducting. Computational studies of optoelectronic and transport properties of energy-renewable devices allow experimentalists to explore novel uses for quick and atomic-level accuracy prediction of photovoltaic materials with diverse crystal structures.

This study provides a comprehensive analytical and graphical exploration of the solitary wave solutions to the (3(+)1)-dimensional Mikhailov–Novikov–Wang integrable (MNWI) equation. We thoroughly examine the solitary wave solutions, emphasising their nonlinear wave propagation, invariant shape and constant velocity. The MNWI equation is used to derive various analytical solutions, including soliton, periodic and rational wave solutions. Additionally, we obtain a heuristic solution for the ((3+1))-dimensional MNWI equation using the Hirota bilinear method, focussing on soliton wave dynamics. The analysis highlights both the mathematical framework and the physical implications of the solutions. By defining bounds on the system’s variables, we assess the overall stability through the Lyapunov function. Nonlinear wave propagation is shown to maintain stability, shape and velocity under bounded conditions. These findings confirm the essential properties and dynamics of solitons. Furthermore, the study reveals complex hybrid solutions through which wave interactions are studied. The outcomes of this work hold significant potential for modelling various physical and environmental phenomena, such as floods, tsunamis and large-scale fluid flows.

This paper explores the matrix modified Korteweg–de Vries (mKdV) integrable models using similarity transformations. The study employs the Lax pair formulation as a foundation, proposing pairs of similarity transformations to reduce the Lax pairs of the Ablowitz–Kaup–Newell–Segur matrix spectral problems, thereby deriving integrable matrix mKdV models. Four illustrative scenarios are discussed to present specific examples of these reduced integrable models.

This paper investigates the soliton dynamics of the geophysical Korteweg–de Vries (GKdV) equation, focussing specifically on different types of soliton solutions that emerge within its framework: trigonometric, hyperbolic and rational solutions. Specifically, the study aims to examine elementary tsunami patterns such as rough waves, singular solitonic waves, periodic waves, sinusoidal waves and kink patterns. The coastal regions have experienced extensive urbanisation and rapid population growth, driven by the advancements of global economy. Consequently, this region is particularly susceptible to severe damages from a range of natural disasters, with tsunamis posing a significant threat. This vulnerability is evident by the occurrence of several devastating tsunami events in the 21st century, which have highlighted the exposure of certain regions to such catastrophic events. In this study, both the first integral method and the sub-ODE method are thoroughly discussed and applied to the GKdV equation. These techniques are employed to derive and analyse exact solutions, providing a deeper understanding of the behaviour and dynamics of the equation in geophysical contexts. The obtained results will enrich the understanding of the dynamics of tsunami models and provide deep insights into the propagation of nonlinear tsunami waves. The Coriolis parameter and the velocity of the travelling wave are considered to have a significant impact on tsunami waves. This study further enhances the understanding of nonlinear wave properties in a geophysical context by integrating phase portrait analysis, waveform characteristics and stability evaluations.

We perform a Lie point symmetry analysis of a time-fractional potential Korteweg–de Vries (FP-KdV) equation with the Riemann–Liouville derivative. By transforming the dependent variable, we map the time-fractional FP-KdV equation to a nonlinear ordinary differential equation (ODE) of fractional order using underlying symmetry generators. We obtain the derivative in the Erdélyi–Kober operator. We then construct the solution of the reduced fractional ODE by applying the power series method. The conservation laws (CLs) for the time-fractional FP-KdV equation are determined via Ibragimov’s non-local conservation method to time-fractional partial differential equations (FPDEs). Solutions for FPDEs via CLs have yet to be explored. Additionally, we present graphical representations of the results obtained using the power series solution method.