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The major objective of this study is to create solitary pattern solutions to the generalised KdV–Zakharov–Kuznetsov equation and fractional-order Triki–Biswas equation using an iterative procedure known as the residual power series method (RPSM). The efficiency of the suggested technique has been demonstrated by example considerations and the results have been graphically demonstrated. This article also discusses the numerical solution of the technique presented. The current method has been demonstrated to be reliable, highly effective and straightforward and can be used in numerous forms of fractional differential equations developed and in scientific domains.

In this paper, we study the higher-order nonlinear Schrödinger equation of surface gravity wave evolution at the critical point (khapprox 1.363). We use dynamic systems to analyse the types of solutions to this equation. Nineteen analytic chirped solutions are obtained by using the chirped wave transformation and polynomial complete discriminant system method. Finally, we add different disturbance terms to the equation and observe chaotic behaviour in the system. These results show that under different parameter conditions the frequency of the surface gravity wave changes as the amplitude changes. Therefore, the chirp (delta omega ) shows a variant of patterns such as singular and periodic structures.

An investigation is carried out to explore the combined effects of Thompson–Troian (T–T) slip and variable mass flux on the mass diffusion of unsteady flow of viscous liquid passing a permeable stretched surface. Constructive/destructive chemical reaction has also been considered in this study. In several engineering sectors including aerodynamics, for HVAC (heating, ventilation and air conditioning) systems, it is essential to have a clear idea about the free stream velocity and how to control it. Trusting on this fact, moving free stream is considered here. This, along with the T–T slip, makes the present research distinct. With the help of ‘similarity transformations’, the governing equations along with the conditions at the boundary are transformed to self-similar forms and using fourth-order Runge–Kutta method with shooting technique by the help of bvp4c package in MATLAB software, solutions are obtained numerically. The influences of relevant parameters on the flow, solute distribution, shear stress and concentration at the surface are analysed in detail. Due to enhanced values of unsteadiness, slip and magnetic parameter, flow velocity decreases. Fluid concentration rises for rising strength of the magnetic field and slip whereas increasing unsteadiness causes the fluid concentration to decrease. Flow velocity is boosted up for rising values of velocity ratio parameter. When the slip parameter increases from 0.1 to 0.5, (36.323%) increase in velocity gradient and (8.262%) increase in surface concentration occur. When the slip parameter increases from 0.1 to 0.5, 36.323% increase in velocity gradient and 8.262% increase in surface concentration occur.

We investigated pressure-induced changes in pyrochlore iridates ((A_2hbox {Ir}_2hbox {O}_7), (A=) Pr, Gd, Dy and Er) using Raman spectroscopy and X-ray diffraction. All four compounds exhibited a pressure-driven isostructural transition associated with the rearrangement of (hbox {IrO}_6) octahedra in the pyrochlore lattice. Interestingly, the critical pressure ((P_textrm{c})) for this transition correlates inversely with the A-site cation radius, (P_textrm{c}) decreased from (sim )10.8 GPa (Er, smallest cation) to (sim )7.5 GPa (Pr, largest cation). Additionally, the bulk modulus systematically decreases with increasing ionic radius of A-site across the (A_2hbox {Ir}_2hbox {O}_7) series. High-pressure Raman spectroscopy revealed anomalous decrease of the linewidth with increasing pressure for Ir–O ((T_{2g}^{4})) and Ir–O–Ir ((A_{1g}) and (E_g)) vibrational modes, suggesting a suppression of electron–phonon coupling due to enhanced electronic bandwidth under pressure.

The current study aims to investigate heat transfer processes in chemically reacting processes, specifically focussing on the flow of an electrically conducting nanofluid over a curved extended surface. The work tries to describe the complex interaction between heat and mass transport phenomena in many applications, such as the biological sciences, catalytic processes and conflagration by including both homogeneous and heterogeneous processes in the framework. Introducing a convective heating strategy is a new technology that may boost circulation phenomena, perhaps leading to improved heat transfer performance. Additionally, the comparison between the Xue and Tiwari–Das models provides helpful insights into their individual suitability and precision in representing the heat transfer mechanism inside the examined system. The boundary layer approximation is used to handle the mathematical equations. Using the proper similarity variables, the controlling partial differential equations (PDEs) are effectively refined into the dimensionless form and computed numerically utilising the Runge–Kutta Fehlberg 4th–5th-order technique. The suggested characteristics of the physical parameters are examined and their relevant behaviour is illustrated graphically. The outcomes declare that the rise in magnetic parameter will decline velocity while enhance thermal profiles. Homogeneous and heterogeneous reaction strengths will decline the mass distribution while heat source/sink, solid fraction and Biot numbers will improve the temperature profile. In all circumstances, the Xue model exhibits a higher rate of thermal dispersion and temperature profile than the Tiwari–Das model.

Given their technological applications, nanoperovskites are an intriguing class of multifunctional materials. To exploit their unique features while avoiding some of their shortcomings, developing low-cost and flexible perovskite(/)polymer nanocomposites with enhanced physicochemical properties attracts various research groups. In this report, two different perovskites, lanthanum ferrite nanoparticles (LF NPs) and lead titanate (LT) NPs were obtained by a solid-state route and mixed with a polyvinyl acetate/polyvinyl chloride (PVAc(/)PVC) thermoplastic blend. LF and LT nanostructuration have been investigated by the transmission electron microscope (TEM) and X-ray diffraction (XRD). The NPs’ good dispersion, uniform distribution on the homogeneous film surface and their complexation with the blend chains were clarified by XRD and field emission (FE)-scan electron microscopy (SEM). The Fourier transform infrared (FT-IR) technique identified the influence of these nanoperovskites on the vibrations of the blend’s characteristic (chemical) groups. The thermogravimetric analysis (TGA) also examined the impact of LF and LT NPs on the films' thermal stability. LT NPs are more effective at manipulating the transmission spectra in the UV–vis and IR regions and shrinking the blend’s optical band gap than LF. The study of the dielectric properties showed that the LT/blend had a higher dielectric permittivity, better conductivity (2.72 ×10⁻⁶ S/cm) and higher energy density (0.48 J/cm³). The absorption index, dual-band gap nature, dielectric loss and dielectric relaxation in the nanoperovskite/polymer were reported. The findings of this study declare that these nanocomposites are the best candidates for photonic devices and supercapacitor fabrication.

In this study, the effects of q-deformed Rosen–Morse potential, particle number and interaction types (two-body, three-body and higher-order (HO) interactions) on Bose–Einstein condensate (BEC) were investigated. The wave functions, which are the solutions of the Gross–Pitaevskii (GP) equation for different conditions, and energies with Shannon information entropies of the BEC systems were calculated, considering attractive interactions between particles. It is found that q-deformed potential values, particle number and interaction types have significant effects on the main dynamics of the systems, while it is found that the high number of particles in the system is more effective than the interactions between the particles, especially, HO interaction is the dominant factor rather than the q deformation value. Also, the change in the entire dynamics of the systems starts around q = 0.1 because the trap potential becomes anti-symmetric at this value.

We consider the nuclear shadowing in deep inelastic scattering (DIS) corresponding to kinematic regions accessible by future experiments at electron–ion colliders. The gluon distribution at small x is obtained using an improved dipole model which depends on the impact parameter for the atomic nucleus and is compared with nCETQ15 parametrisation group. The nuclear shadowing at small x is defined within the colour dipole formalism with respect to the mass number A. Its behaviour is predicted for light nuclei in a wide range of the impact parameter b and the transverse dipole size r. The nuclear saturation can be observed at large-r (small (mu ^2)). The behaviour of the nuclear ratio (sigma ^{A}_{textrm{dip}}/sigma _{0}) using our model is similar to the Golec–Biernat–W(ddot{textrm{u}})sthoff (GBW) model in a wide range of r for light and heavy nuclei at small x.

Through the application of mathematical epidemiology principles, the formulation of the soft drugs model is established, and the complete dynamics of this deterministic model are contingent upon the crucial parameter called the basic reproduction number, denoted as (R_{0}^{d}). The stochastic soft drug epidemic models are developed by considering the parametric and non-parametric stochastic perturbation techniques. Dynamics of the two different stochastic models are determined using the analog stochastic thresholds (R_0^{s_{1}}), (R_0^{s_{2}}), respectively. Introducing suitable Lyapunov functionals enables us to establish sufficient axioms for the extinction and permanence of soft drug users in both deterministic and stochastic models. Moreover, the sensitivity of the deterministic and stochastic thresholds to some important parameters involved in the models is illustrated. For the verification of our theoretical results, we develop some numerical simulations using the Euler–Maruyama scheme.

The present investigation examines the behaviour of compact relativistic objects characterised by static and spherically symmetric space–time for neutral anisotropic matter distribution. More specifically, we consider an equation of state (EoS), in which density and radial pressure are connected with each other quadratically. By smoothly matching the interior space–time with the exterior at the stellar surface, the appropriate values of the constant parameters for physically realistic solutions are obtained to model various compact stars. We explore the physical behaviour of compact stellar models SMC X-4, Vela X-1, CEN X-3, PSR J1614-2230, LMC X-4 and EXO 1785-248. Further, we describe several features of the compact stellar systems that exhibit physically acceptable attributes with no singularity. All important stability criteria, such as the energy conditions, causality conditions, Buchdhal condition and the adiabatic index are fulfilled by our neutral anisotropic compact star models. An in-depth comprehension of the physical characteristics of the proposed solution has been achieved through meticulous analytical and graphical examinations. By utilising this solution, the masses and radii of six compact stellar candidates mentioned above are optimised with the observed values obtained experimentally. The derived solution might be useful to enhance the understanding of the strong-field regimes and self-gravitating entities.