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Genralised B-type Kadomtsev–Petviashvili (gBKP) equation corresponds to the weak dispersive nature of the propagating waves in quasi-media and fluid mechanics. In this paper, a collection of exact soliton and periodic wave solutions are obtained for the ((3 + 1))-dimensional gBKP equation using the well-known generalised exponential rational function (GERF) method. Several classes of exact soliton and periodic solutions are derived using trigonometric and hyperbolic functions by employing this method. A graphical representation of the solutions is also presented to analyse the dynamics of the system. With the help of the computational software Mathematica, the visualisations for the wave configuration of various solutions are presented using three- and two-dimensional plots. The plots represents the wave profile of a wide range of singular soliton, multi-solitons and periodic solitons obtained for the considered equations by taking appropriate values for the associated parameters. The collection of solutions listed in the article signify the importance and possible application of GERF method to a wide variety of nonlinear differential equations in physical phenomena.

In this paper, we study the temperature evolution of the Friedmann–Robertson–Walker (FRW) Universe filled with viscous generalised Chaplygin gas (VGCG) as a model of dark energy. We started the thermodynamical treatment of the VGCG, which is given by the equation of state (p=-frac{A}{rho ^{alpha }}) with bulk viscosity in the framework of the Eckart theory. We investigated it in the cosmological model using the FRW metric in flat space–time, and we were able to determine its temperature as a function of redshift z. Besides, the expression for the fluid’s temperature in terms of redshift and the viscosity parameter (xi _{0}) is derived. In our computation, we assumed that the value of the parameter (Omega _{x}) would be 0.7 and that the current value of the temperature of the microwave background radiation would be given by (T_{0}=2.7) K. Using the decoupling redshift value ((zapprox 1100)) and the viscous parameter, the decoupling temperature is computed. The optimum choices for the remaining parameters are (alpha =0.25), (Omega _{x}=0.75), (xi _{0}=-0.1930), yielding a decoupling temperature of (T(z=1100)approx 4000) K and a redshift of (zapprox 0.25). We also compute the decoupling temperature in this model at (ddot{a}=0) and (T_{0}=2.7) K. In terms of z and (xi _{0}), we also examined other parameters, such as the Hubble parameter, the equation of state parameter, the adiabatic speed of sound, jerk, snap and Om diagnostic parameters. These values are then compared with the outcomes of earlier research on modified Chaplygin gas (MCG) and other Chaplygin gas. We have shown that this model is thermodynamically stable for (xi _0 < 0) in the FRW Universe and studied the validity of the generalised second law of thermodynamics on the apparent and event horizons of the Universe in the FRW Universe dominated by various Chaplygin gas fluids. However, a perfect fluid with (omega _{textrm{eff}}<-frac{1}{3}) would produce an acceleration phase but might not produce a feasible dark energy epoch in the early and late stages of the Universe that is consistent with the observational data.

This study investigates the free convective flow of a second-grade incompressible viscous fluid through a vertical duct filled with a porous medium, driven by an oscillating pressure gradient parallel to the channel plates. The flow dynamics are influenced by periodic temperature changes on one of the plates and a significant temperature differential between the plates, which introduces a heat source into the system. Additionally, the effect of duct inclination on the convective flow is explored, as the inclination angle modifies buoyancy forces, thus impacting velocity and temperature profiles. The analysis provides insights into how key parameters, such as the heat source intensity, inclination angle and properties of the second-grade fluid, affect the temperature field, phase angles, velocity profiles and heat transfer rates. A comprehensive visual representation illustrates the effects of amplitude of these factors on the thermal and flow characteristics, highlighting the complex interactions between fluid elasticity, porous media resistance and thermal gradients.

The applications of the present findings are extensive and transformative and these findings help in improving heat transfer in thermal industrial systems, facilitating efficient operation of solar collectors, electronic cooling devices, as well as targeting and destroying cancer cells in hyperthermia treatment in the medical field. This study analyses the tangent hyperbolic nanofluid with tetrahybrid nanoparticle that is the combination of (hbox {Al}_2) (hbox {O}_3), Ag, (hbox {TiO}_2) and ZnO over horizontal and exponentially stretching/shrinking cylinder filled with non-Darcy porous medium. Electromagnetohydrodynamics (EMHD), Arrhenius activation energy, thermal radiation, heat source and chemical reaction were considered. The fundamental equations of non-linear ordinary differential equations (ODEs) were derived from the partial differential equations (PDEs) with similarity variables and fifth-order Runge–Kutta–Fehlberg method with shooting technique was performed. From the model, we obtained increase in temperature profile for magnetic parameter and radiation parameter and increase in concentration profile for activation energy parameter. Shape factor analysis on Nusselt number and Sherwood number was done and compared. Heat and mass transfer rate was investigated by changing the shapes of the nanoparticle on exponential and horizontal cylinder to get good results.

This study uses spin coherent states to generate two- and three-partite entangled states. We then investigate the entanglement and correlation of these systems when one component undergoes uniform acceleration. The entanglement of bipartite and tripartite states is quantified using concurrence and 3-tangle, respectively, while the mutual entropy is used to evaluate the system correlation. The findings indicate that the entanglement and correlation decrease as a function of the acceleration parameter. Furthermore, a comparison of entanglement and mutual entropy reveals that the correlation of the bipartite system is predominantly manifested as entanglement. However, the quantum correlation of the tripartite system is of an entanglement type within a certain range of the coherence parameter, but outside this range, it transforms into a classical type.

The main aim of this paper is to obtain the approximate series solution of the time-fractional nonlinear Zakharov–Kuznetsov (TFZK) equations using the Laplace residual power series (LRPS) method. LRPS method is a coupling where Laplace transformation is gracefully combined with the residual power series method. One important feature of the LRPS technique is that it uses the concept of limits at infinity, which help us to determine the unknown coefficients of the convergent power series solution. Caputo fractional derivative is used in the formulation of Zakharov–Kuznetsov (ZK) equations. The ZK equations with time-fractional derivative have significant implications in the study of wave dynamics in ocean-based coastal regions, making their approximate solution essential for understanding complex wave phenomena. To validate the effectiveness of the LRPS approach, we analysed two different forms of the TFZK equation. Simultaneously, we visually captured the physical behaviour of the approximate solution using various tables and plots for different fractional orders. Numerical simulation is demonstrated using Maple and Matlab. Comparative analyses were performed with other existing methods, demonstrating the superiority of the LRPS method in solving TFZK equations.

The spontaneous condensation of excitons in the excitonic insulating phase has been reported in (hbox {Ta}_2hbox {NiSe}_5) (TNSe) below 325 K. In this context, we present the temperature-dependent optical pump–optical probe spectroscopy of (hbox {Ta}_2hbox {NiSe}_5), with the focus on coherent phonon (CP) dynamics. In addition to the fast relaxation process involving excitonic recombination, we observe a systematic behaviour for the slow relaxation process associated with the relaxation of hot phonons. The asymmetry parameter and cubic anharmonicity of the 3 THz mode demonstrate the structural transition across (T_C=325) K, whereas the nature of the order parameter and asymmetry of 2 THz modes reveal its coupling with the excitonic phase of TNSe. Coherent phonon modes display less anharmonicity than the corresponding Raman modes. Continuous wavelet transform (CWT) reveals that the peak time (t_{textrm{peak}}) of the phonons is similar for all modes except the 3 THz mode. The temperature dependence of (t_{textrm{peak}}) for the M3 mode exhibits a possible role of excitonic condensate below (T_C) in the formation of quasiparticle (phonon). CWT analysis supports the time-dependent asymmetry of the M3 mode caused by photoexcited carriers. This study illustrates the role of photoexcited carriers in depicting a structural transition and dressing of coherent phonons, hence, demonstrating many-body effects.

In this paper, the high dispersive nonlinear Schrödinger equation with parabolic law nonlinearity, which is significant in the study of nonlinear optics, is discussed using two different approaches, namely the unified method and the improved F-expansion method. As an outcome, scores of complex analytical exact optical solutions are offered. Specifically, three types of solutions in polynomial form are constructed via the unified method. A succession of hyperbolic trigonometric, trigonometric and rational solutions are built with the assistance of the improved F-expansion method. Further, we draw two-dimensional, three-dimensional and contour images for some selected solutions so as to make a more comprehensive and systematic exploration for wave propagation.

The main goal of this paper is to investigate the soliton dynamics of the stochastic Gross–Pitaevskii equation (SGPE), which is forced by multiplicative white noise by using new extended direct algebraic method. The SGPE serves as a fundamental model in the study of Bose–Einstein condensates (BECs) and related systems, capturing complex nonlinear interactions in ultra-cold atomic gases. Incorporating random fluctuations into the SGPE framework reflects real-world scenarios where environmental noise plays a significant role. Utilising a direct algebraic method enables a comprehensive exploration of the interplay between deterministic soliton behaviour and stochastic perturbations. Through analytical analysis, we unveil the intricate effects of random fluctuations on soliton formation, propagation and stability. This paper not only advances our fundamental understanding of soliton dynamics in stochastic systems but also provides practical tools for harnessing and controlling soliton behaviour in complex, fluctuating environments.

The current study explores Eyring–Powell nanofluid (EPF) across a curved stretching surface (CSS) in the presence of micro-organisms, thermal radiation and Lorentz force. It has implications in advanced engineering and biomedical applications. Understanding non-Newtonian fluid behaviour is crucial for optimising heat and mass transfer (HMT), thermal management and targeted drug delivery. We employed Lorentz’s force, chemical reaction and thermal radiation on the fluid flow. As is well known, HMT over the CSS is relevant in biomedical engineering for applications like drug delivery systems and medical implants. The fundamental nonlinear partial differential equations (PDEs) are converted to ordinary differential equations (ODEs) by applying suitable similarity transform and numerically solved by using the Chebyshev spectral method (CSM). Numerical results are concluded by employing tables in attractive representations, which are discussed for different values of non-dimensional curvature radius, permeability coefficient, Eyring–Powell liquid factors, radiation factor, Brownian coefficient, thermophoresis factor, heat generation (absorption) factor, chemical reaction factor, Schmidt factor, Dufour numeral, Soret numeral, magnetic factor, Eckert numeral, bio-convection, Lewis numeral, Peclet numeral and bio-convection factor on the velocity, temperature, concentration and spreading of micro-organisms. The results indicate that the velocity and concentration increase with the rise of curvature radius and permeability coefficient, whereas the distributions of temperature and micro-organisms decrease as these parameters increase. Moreover, all the temperature, concentration and micro-organisms’ distributions increase as the Brownian coefficient increases. Finally, the temperature distribution increases with the assessment of the thermophoresis factor. Conversely, the concentration and propagation of micro-organisms decrease.