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This exploration aims to extract some new exact solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation (BKPE) that plays a significant role in fluid dynamics. Based on the N-soliton solutions extracted by the Hirota bilinear method, the Y-shape and X-shape soliton solutions and the breather wave solutions are derived by assigning resonant conditions and conjugate conditions, respectively. Furthermore, three powerful tools, namely the Bernoulli sub-equation function method, Wang’s direct mapping method-II and Kudryashov method, are employed to explore the diverse travelling wave solutions, which includes the kink solitary wave, anti-kink solitary wave, periodic wave and singular wave solutions. The wave structures of the attained solutions are displayed as diagrams using Maple. As we all know, the outcomes presented in the study are all brand new and have not been reported in other work, which can enable us to better understand the dynamic behaviours of the considered equation.

Choosing a specific direction for the propagation of laser field waves often presents a challenge for researchers studying laser-assisted ultrafast quantum processes. They are faced with the question of why exactly a particular direction and not another. This paper resolves the discussion in this issue regarding decay processes. Therefore, we study theoretically the pion decay process in the presence of a circularly polarized laser field propagating along an arbitrary general direction. Using the first Born approximation and the Dirac-Volkov states for charged particles, we derive an analytic expression for the decay rate. Our results show that, when the pion is at rest, the direction of the laser field has no significant effect on the decay rate, justifying the common practice of choosing a convenient direction in previous studies. However, when the pion is in motion, the decay rate is affected by the laser wave vector’s orientation relative to the pion’s momentum. The effect is more pronounced when the wave vector is collinear with the pion’s motion than when it is perpendicular. This study generalizes previous results found for a field with a wave vector along the z-axis in [Phys. Rev. D 102, 073006 (2020)] and provides a theoretical foundation for future investigations into laser-assisted decay processes involving moving particles. The influence of the laser field on the total decay rate has also been analyzed and discussed.

In the cone–disk system, the apex of the cone is in contact with the disk, making a conical region, in which the fluid flow is analysed. This type of flow problem has a variety of biomedical application including DNA sequencing, biochemical detection, cell analysis, conical diffusers, viscosimeters, etc. The effect of Hall current and radiation on the flow of blood containing gold nanoparticles is theoretically analysed in a cone–disk system for a single-phase nanofluid model. Four configurations of the cone–disk system, including stationary disk and rotating cone, stationary cone and rotating disk, co-rotation of disk and cone and counter-rotation of disk and cone, are studied for the gap angle (frac{pi }{4}). The non-linear partial differential equations describing three-dimensional axisymmetric flow in a cone–disk system are converted into nonlinear ordinary differential equations using the one-parameter Lie group approach. The self-similar model is then solved numerically using the bvp5c package of MATLAB and shown graphically to analyse the influence of various parameters involved in the study for all four configurations of the cone–disk system. It is observed that rotation of the disk/cone gives rise to high centrifugal forces resulting in an outward radial flow. Further, it is noted that Hall current enhances the velocity and radiation parameter reduces the temperature.

The primary aim of the present paper is to analyse the Reiner–Philippoff hybrid nanofluid (HNF) flow over a stretching(/)shrinking sheet under the influence of thermal radiation and suction. A set of partial differential equations is used to describe the model, which is then reduced to non-dimensional ordinary differential equations through similarity transformations and solved computationally with the help of the bvp4c function. A graphical investigation examines the effects of various parameters, including the magnetic parameter, suction, Philippoff fluid parameter, Eckert number, radiation parameter, porosity parameter and Bingham number on velocity, temperature, skin friction and the local Nusselt number. The results show that as the Bingham number, Philippoff fluid parameter and stretching(/)shrinking parameter increase, the velocity profiles exhibit an upward trend. In addition, increasing the magnetic, porosity and suction parameters leads to higher absolute values of the skin friction coefficient. It is also noted that the rate of heat transfer increases up to 14.11% with an increase in the radiation parameter. The novel findings of this study provide a deeper understanding of HNF behaviour, which can facilitate the optimisation of heat transfer systems in industrial and engineering applications.

This research reveals the novel types of exact wave solutions of the nonlinear Gardner–Kawahara (G–K) model in the concept of truncated M-fractional derivative. The G-K model, which is also called the extended Korteweg–de Vries (KdV) model, explains the solitary wave propagation in media, notation in plasmas, notation in shallow-water waves along surface tension and notation of magneto-acoustic waves. For our purpose, two techniques, the unified and the Sardar sub-equation techniques are applied. As a result, new types of exact wave solitons having periodic, dark–bright, periodic, kink are obtained. Some of the obtained solutions are represented through two- and three-dimensional and contour plots. The effect of the truncated M-fractional derivative (TMFD) is explained by plots. Stability of a concerned equation is checked by applying stability analysis. Moreover, the modulation instability analysis of the governing equation is also performed, which proves that the model and the obtained results are stable as well as exact.

The magnetic behaviour of a three-electron quantum dot(/)ring system is analytically investigated with electron–electron (e–e) interaction taking into account the Rashba effect and magnetic field. The Jacobi transformation has been employed to separate the Hamiltonian of the system into relative motion and the centre of mass. The Schrödinger equation is analytically solved and energy spectra are obtained. Then, the magnetisation and susceptibility are calculated. The magnetisation decreases by rising the magnetic field without and with spin–orbit interaction (SOI) and also without e–e interaction. The Rashba effect slightly modifies the magnetisation of the system without e–e interaction. The susceptibility displays a peak structure as the magnetic field changes from low values to high values. The susceptibility sign is negative by considering e–e interaction and without the Rashba effect and its value decreases by rising the magnetic field. The susceptibility displays a transition from diamagnetic to paramagnetic by considering the e–e term and the Rashba effect.

We have demonstrated that the relationship between the deep inelastic scattering structure functions remains stable for a nuclear target with mass number A at (x{le }10^{-3}). Numerical results have been provided for the specific nuclei (^{12})C and (^{208})Pb using the nuclear PDF parametrisations incorporated in the HIJING2.0 model. These findings are within the electron–ion collider kinematic acceptance for heavy ion running. The ratio (R^{A}_{F_{L}}) is determined as the ratio (R^{A}_{F_{2}}) based on the HIJING2.0 model.

In the present work, the capture and fission dynamics of (Z=) 102 and 103 nuclear systems are investigated. The coupled channel model and the extended Wong model are used to address nuclear capture as well as fission cross-sections of (^{48})Ca(+) (^{208})Pb (leading to the composite system (^{256}_{102})No(^*)) and (^{50})Ti(+^{208})Pb (resulting in (^{258}_{104})Rf(^*)) reactions in reference to the available experimental data. Furthermore, the isotopic analysis of the (Z =) 102 nucleus is performed by changing the mass of the projectile–target (p–t) nuclei that leads to the synthesis of (^{252,254,256})No(^*) composite systems. The study suggests relatively higher cross-sections and compound nucleus formation probability ((P_{textrm{CN}})) values for the reactions in which (^{48})Ca projectile is involved with (^{208})Pb. Also, with a decrease in neutron number for Ca projectile (i.e., (^{48,46,44})Ca with (^{208})Pb target) the fission cross-sections drop by 40(%) which otherwise for Pb target ((^{208,206,204})Pb with (^{48})Ca projectile) is 10(%). Subsequently, an attempt is made to predict the nuclear capture and fission data of (Z=) 103 (Lr(^*)) nucleus within the mass domain of 249u to 261u (i.e., (^{249,253,257,261})Lr(^*)) using various heavy-ion fusion reactions. Along with this, the decay profiles of (^{249-261})Lr(^*) composite systems are examined within the framework of the dynamical cluster decay model (DCM) in reference to the fragmentation potential, preformation probability and average total kinetic energy ((langle mathrm TKErangle )) distribution. Apart from traditional Pb-valley, an additional dip around the entrance channel mass asymmetry of (eta approx 0.4) and (eta approx ) 0.2 is also noted for the reactions under consideration.

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.