Narrow Results

In this paper, we implement the Einsenhart–Duval lift in scalar–tensor gravity as a means to construct integrable cosmological models and analytic cosmological solutions. Specifically, we employ a geometric criterion to constrain the free functions of the scalar–tensor theory such that the field equations can be written in the equivalent form of linear equations. This geometric linearization is achieved by the introduction of an extended minisuperspace description. The results are applied to construct analytic solutions in modified theories of gravity such as the $f(R)$-theory and the hybrid metric-Palatini $f({ℛ})$-gravity.

We investigate a generalized variable-coefficient modified Korteweg–de Vries model with perturbed factor and external force (vc-GmKdV) describing fluid dynamics and space plasmas. In this paper, we propose an extended variable-coefficient balancing-act method (Evc-BAM), which is concise and straightforward, to obtain the generalized analytic solutions including solitary wave solution of the vc-GmKdV model with symbolic computation. Meanwhile, using the Evc-BAM, we obtain an auto-Bäcklund transformation for the vc-GmKdV model on the relevant constraint conditions of the coefficient functions. Using the given auto-Bäcklund transformation, the solutions of special equations for the vc-GmKdV model are also obtained as the variable-coefficient Korteweg–de Vries (vc-KdV) equation, the generalized KdV equation with perturbed factor and external force (GKdV), the variable-coefficient modified Korteweg–de Vries (vc-mKdV) equation, and the variable-coefficient cylindrical modified Korteweg–de Vries (vc-cmKdV) equation, respectively.

In this note an analytic integration is obtained for the differential equation governing the scalar-field-dependent mass in a hairy binary black hole model, in the context of the Einstein–Maxwell–dilation theory, which gives a closed-form formula-level description of the mass function. We also identify a particular solution which attracts all solutions of the mass-governing equation exponentially rapidly in large-dilaton-field limit.

This study deals with the physical aspects of the gravitationally decoupled solutions under $f(\mathcal{ℛ})$ gravity scenario. In doing so, charged anisotropic matter composition is assumed as the parent (seed) source for the static spherically symmetric configuration. Commencing with the Kuchowicz ansatz for the charged static parent matter formation, we establish the Karmarkar condition to thoroughly address the deformed functions and the gravitational aspects of the compact spheres. Besides these, null-complexity and isotropized conditions will enforce to grasp the system’s stability by the inclusion of charge and $\mathcal{ℛ}+\varpi {\mathcal{ℛ}}^2$ factors through graphical trends.

Roll coating is a popular method for applying a thin coating film to a continuous substrate, such as paper or foil. This study aims to investigate analytically the fluid flow through counter rotating rolls using a non-Newtonian model. The governing equation for the constitutive of the Oldroyd-B as a non-Newtonian fluid with momentum equation has been discovered. The nondimensionalizing of the fluid flow equations is done by using suitable dimensionless parameters. The equations are then simplified by using Lubrication Approximation Theory (LAT) to obtain the solution for various quantities. Analytical solutions for the velocity distribution, pressure and pressure gradients have been obtained by regular perturbation method. Numerical integration has been used to calculate separation point, coating thickness, separation force and power input of the fluid. The effect of involved parameter such as Weissenberg number We and viscosity on velocities, pressure gradient and pressure is presented in a variety of graphs and several other results are shown in tables. It has been observed that as the modified capillary number $N_{C{a}_2}$ increases, the separation point moves toward the nip region, whereas the coating thickness declines. It has been witnessed that the We serves as the controlling parameter for flow rate, pressure distribution and power input, whereas for the coating thickness, the separation force increases, which are important for coating industries.

By applying the two efficient mathematical methods particularly with regard to the classical Lie symmetry approach and generalized exponential rational function method, numerous exact solutions are constructed for a (2 + 1)-dimensional Bogoyavlenskii equation, which describes the interaction of Riemann wave propagation along the spatial axes. Moreover, we obtain the infinitesimals, all the possible vector fields, optimal system, and Lie symmetry reductions. The governing Bogoyavlenskii equation is converted into various nonlinear ordinary differential equations through two stages of Lie symmetry reductions. Accordingly, abundant exact closed-form solutions are obtained explicitly in terms of independent arbitrary functions, rational functions, trigonometric functions, and hyperbolic functions with arbitrary free parameters. The dynamical behavior of the resulting soliton solutions is presented through 3D-plots via numerical simulation. Eventually, single solitons, multi-solitons with oscillations, kink wave with breather-type solitons, and single lump-type solitons are obtained. The proposed mathematical techniques are effective, trustworthy, and reliable mathematical tools to work out new exact closed-form solutions of various types of nonlinear evolution equations in mathematical physics and engineering sciences.

Nonlinear evolution equations of arbitrary order bearing a significantly broad range of capability to illustrate the underlying behavior of naturalistic structures relating to the real world, have become a major source of attraction of scientists and scholars. In quantum mechanics, the nonlinear dynamical system is most reasonably modeled through the Schrödinger-type partial differential equations. In this paper, we discuss the (2+1)-dimensional time-fractional nonlinear Schrödinger equation and the (1+1)-dimensional space–time fractional nonlinear Schrödinger equation for appropriate solutions by means of the recommended enhanced rational $(G^{\prime }/G)$-expansion technique adopting Cole–Hopf transformation and Riccati equation. The considered equations are turned into ordinary differential equations by implementing a composite wave variable replacement alongside the conformable fractional derivative. Then a successful execution of the proposed method has been made, which brought out supplementary innovative outcomes of the considered equations compared with the existing results found so far. The well-generated solutions are presented graphically in 3D views for numerous wave structures. The high performance of the employed technique shows the acceptability which might provide a new guideline for research hereafter.

A model Hamiltonian, motivated by QCD, is investigated in order to study only the quark sector, then only the gluon sector and finally both together. Restricting to the pure quark sector and setting the mass of the quarks to zero, we find analytic solutions, involving two to three orbitals. Allowing the mass of the quarks to be different to zero, we find semi-analytic solutions involving an arbitrary number of orbitals. Afterwards, we indicate on how to incorporate gluons.

The focus of this paper is on Kawahara equation (KE) which models diverse variety of waves enforced in many branches of applied sciences. Symmetries to the considered equation are successfully obtained by practicing nonclassical method. According to nonclassical symmetries, KE has been reduced to numerous ODEs. Further, these ODEs are treated such that new analytic solutions are determined by applying power series, ansätz and $(\frac{G^{\prime }}{G^2})$-expansion method.

The aim of this study is to explain theoretically the role of ciliary motion on the transport of epididymal fluid through the ductus efferentes of the male reproductive track. For this purpose, a mathematical model has been developed for the flow of a non-Newtonian fluid in an axisymmetric tube due to metachronal wave of cilia motion for the more realistic consequences. Carreau viscous fluid model is considered to see the rheological effects on the pumping characteristics of the flow. Regular perturbation method has been employed to obtain the analytical expressions for the stream function, the velocity field and a relation between the pressure difference and the volume flow rate. It is found that the volume flow rate is influenced significantly by Weissenberg number W_e and the cilia length parameter ε. The computational results are presented graphically to see the effects of various physical parameters. Finally, the analysis is applied and compared with the observed value of the flow rate of spermatic fluid in the ductus efferentes of the male reproductive track. The volume flow rate is reported closed to the estimated value 6 × 10^-3 ml/h in the human ductus efferentes when W_e = 0.5 and ε is near by 0.25.