International Journal of Geometric Methods in Modern Physics

In this paper, we conduct a thorough investigation into holomorphic Riemannian maps from nearly Kaehler manifolds. We determine the necessary and sufficient conditions for these maps to be harmonic. In addition, we explore the scenario where the total manifold admits a Ricci soliton, analyze the properties of the holomorphic Riemannian maps in this context. We also establish several conditions under which the fibers of these maps admit Ricci solitons and trivial Ricci solitons.

We established an anisotropic Bianchi type-I dark energy model in this investigation’s $f(R,L_m)$ gravity, where $f(R,L_m)$ is an arbitrary function of the Ricci-scalar curvature $R$ and the matter Lagrangian $L_m$. For the sake of our analysis, we have taken a particular form of this function, which is represented by the equation $f(R,L_m)=\frac{R}{2}+\alpha L_m^n-\mathrm{\Lambda }$, where $\alpha ,n$ are model free parameters, and $\mathrm{\Lambda }$ is the “cosmological constant”. In order to derive the Hubble function $H(z)$ in terms of redshift $z$, we analytically solved the field equations and established a connection between the energy parameters ${\mathrm{\Omega }}_m,{\mathrm{\Omega }}_k,{\mathrm{\Omega }}_{\mathrm{\Lambda }}$ and $\omega$. By using the ${\chi }^2$-test, we compared this Hubble function to $H(z)$ datasets to find the model and energy parameters that fit the data the best. Also, we have analyzed our result with statefinder and Om diagnostic analysis that suggests the model to be a quintessence dark energy model and tends to $\mathrm{\Lambda }$CDM model in late time.

Chen–Lee–Liu (CLL) equation has many applications in optical fibers as well as in plasma physics. It describes the propagation of optical pulse in the monomode fiber. CLL equation is a modification of the nonlinear Schrödinger equation. In this paper, the nonlinear CLL is explored using generalized projective Riccati equation method and two variable $\left(\frac{G^{\prime }}{G},\frac{1}{G}\right)$-expansion method. Consequently, many new solitary wave solutions are achieved in a unique way. These solutions include dark solitons, bright solitons and periodic wave solutions which describe the related physical phenomena. In the end, these solutions are presented in the form of 3D and 2D plots in order to elaborate the wave structure corresponding to the obtained solutions.

Let $(M^n,F,m)$ be a compact Finsler manifold. This paper will obtain a global estimate and a differential Harnack inequality for positive solutions to the Newell–Whitehead–Segal equation

In this paper, we consider the Yang–Mills–Higgs flow for twisted Higgs pairs over Kähler manifolds. We prove that this flow converges to a reflexive twisted Higgs sheaf outside a closed subset of codimension $4$, and the limiting twisted Higgs sheaf is isomorphic to the double dual of the graded twisted Higgs sheaves associated to the Harder–Narasimhan–Seshadri filtration of the initial twisted Higgs bundle.

The construction of compact star models with quintessence and cloud of strings anisotropic fluid lays the foundation for the research presented in this paper, which focuses on the ansatz of f(Q) gravity. We utilized a spherically symmetric spacetime to derive the field equations incorporating quintessence and cloud of strings anisotropic matter fields. The well-known Karmarkar condition was employed to obtain the gravitational components of the spherically symmetric spacetime. The constant parameters used in the study were obtained by applying junction conditions on the interior and exterior spacetimes. We used the mass and radius of $PSRJ1614-2230\&SMCX-1$, which are already present in the literature. Afterward, we calculated the important properties of quintessence stars in the presence of cloud of strings to ensure the stability and physical presence of compact models. To achieve this goal, we studied features such as energy density, quintessence density, pressure profiles, gradients, anisotropic factor, energy conditions, sound speeds, TOV forces, EoS components, mass function, compactification and redshift.

In this paper, we investigate various types of symmetries and their mutual relationships in Hamiltonian systems defined on manifolds with different geometric structures: symplectic, cosymplectic, contact and cocontact. In each case, we pay special attention to non-standard (non-canonical) symmetries, in particular scaling symmetries and canonoid transformations, as they provide new interesting tools for the qualitative study of these systems. Our main results are the characterizations of these non-standard symmetries and the analysis of their relation with conserved (or dissipated) quantities.

By making use of two viable Lagrangian $f(T,{𝒯})$ models, we investigate the behavior of the state parameter of the interacting viscous dark energy. We, from constant deceleration parameter, explore the cosmological implications of the viscosity and interaction between the dark energy and dark matter in terms of redshift. We then construct the viscosity and the interaction parameters that are respectively parameterized by $d_o^{\eta }({\rho }_{\mathrm{\text{DE}}})$ and $\xi$ and obtain interesting results. Later, we investigate the behavior of some bulk viscosity models describing little rip and pseudo rip future singularities within $f(T,{𝒯})$ modified gravity. We obtain interesting gravitational equations of motion for viscous dark energy coupled with dark matter. The solution of these equations gives us an analytic expression for characteristic properties of these cosmological models.

Ecological system is the interaction of biological community with other organisms and their physical environments. One of the important models is spatiotemporal prey–predator model of Michaelis–Menten-type functional response and reaction diffusion with constant harvest rate. This paper investigates the spatiotemporal structures of ratio-dependent prey and predator densities under different constraint conditions and suitable parameters. The ${\varphi }^6$ model expansion technique is followed to extract these densities. The prey and predator densities behave differently depending on the diffusion coefficients and other parametric ratios. The 3D and 2D behavior of these densities are also plotted and observed. These results may help for better understanding to study the biological community in a real marine environment or ecological system.

In this study, we demonstrate that when three distinct moving space-like curves with the time-like binormal vectors satisfy the generalizations of the Heisenberg spin chain model, these models are equivalent to the third-order system of the AKNS hierarchy and the complex KdV-type equations.

This paper addresses the new $(3+1)$-dimensional Mikhailov–Novikov–Wang (MNW) equation with arbitrary order derivative and presents novel exact solutions of it by implementing $exp(-\phi (\xi ))$-expansion, modified Kudryashov, generalized $(G^{\prime }/G)$-expansion, and modified extended tanh-function methods. This equation emphasizes significant connection between the integrability and water waves’ phenomena. Employing the conformable derivative definition, a variety of soliton (bright, dark, anti-kink) solutions of the model are obtained. Therefore, it would appear that these approaches might yield noteworthy results in producing the exact solutions to the fractional differential equations in a wide range. In addition, 2D, 3D, and contour plots of the solutions are drawn for specific values to demonstrate the physical behaviors of the solutions.

Galactic rotation curve is a powerful indicator of the state of the gravitational field within a galaxy. The flatness of these curves indicates the presence of dark matter (DM) in galaxies and their clusters. In this paper, we focus on the possibility of explaining the rotation curves of spiral galaxies without postulating the existence of DM in the framework of $f({ℛ},T)$ gravity, where the gravitational Lagrangian is written by an arbitrary function of ${ℛ}$, the Ricci scalar and of $T$, the trace of energy–momentum tensor $T_{\mu \nu }$. We derive the gravitational field equations in this gravity theory for the static spherically symmetric spacetime and solve the equations for metric coefficients using a specific model that has minimal coupling between matter and geometry. The orbital motion of a massive test particle moving in a stable circular orbit is considered and the behavior of its tangential velocity with the help of the considered model is studied. We compare the theoretical result predicted by the model with observations of a sample of 19 galaxies by generating and fitting rotation curves for the test particle to check the viability of the model. It is observed that the model could almost successfully explain the galactic dynamics of these galaxies without the need of DM at large distances from the galactic center.

Reconstruction of Lagrangian functions present in the action of modified gravity theories is one of the most captivating subjects in recent cosmology. This paper reconstructs the form of Lagrangian function of some teleparallel theories based on a recently proposed holographic dark energy model namely new Tsallis HDE. For this purpose, we assume ordinary matter contents as perfect fluid with background geometry as flat FRW spacetime. On the first place, we reconstruct $f(T)$ function by taking some well-known IR cutoff choices into account like Hubble radius, event horizon, Granda–Oliveros cutoff and conformal time as different cases. Moreover, we consider two entropy corrected forms of new Tsallis HDE with the simplest choice for IR cutoff. We explore the graphical behavior of different cosmic quantities, e.g. dark energy EoS parameter, the generalized second law of thermodynamics, the null energy condition, speed of sound and trajectories in ${\omega }_T-{\omega }_T^{\prime }$ plane for these reconstructed solutions and discuss their viability. Then we extend our work to $f(T,B)$ theory and reconstruct the Lagrangian function for new Tsallis HDE with three simple choices of IR cutoff (Hubble radius and event horizon), and Granda–Oliveros cutoff and discuss the significance of obtained solutions graphically through same cosmic measures. It is found that presented models are consistent with the recent cosmic data values, however, stability can be achieved in some certain cases only.

Motivated by the work of Nojiri et al. [Phys. Lett. B 797 (2019) 134829], we utilize the holographic principle in the early universe to realize the holographic origin through inflation. A similar argument can be made for its well-researched late-time application, and the early-time horizon contraction naturally boosts holographic energy density at inflationary scales. After accounting for the IR cutoff adjustment and using holographic Ricci dark energy as the inflationary fluid, we have shown the significance of ${\mathrm{\Lambda }}_{\mathrm{\text{UV}}}$ in the inflation realization. For holographic Ricci dark fluid’s potential to realize inflation, several restrictions were derived. The e-folding number was used to discuss inflationary observables and determine the slow-roll parameters. The study covered the effects of reconstructing the IR cutoff and the potential for inflation to be realized after taking into account holographic Ricci dark energy as a special instance of the most generalized Nojiri–Odintsov holographic dark energy [S. Nojiri and S. D. Odintsov, Gen. Relativ. Gravit. 38 (2006) 1285–1304]. Additionally, some time intervals for the potential of inflation have been calculated, and the behavior of the equation of state parameter has also been discussed.

In this paper, we extend the result of [A. Fring et al. J. Phys. A 43 (2010) 345–401] in Noncommutative phase-space (NCPS). We compute the non-Hermitian Hamiltonian of a harmonic oscillator in NCPS. We construct a new $PT$-symmetry in NCPS and prove that the system does not possess a broken $PT$-regime. We then compute the eigenvalue spectrum of the non-Hermitian Hamiltonian of the system.

The aim of this paper is to examine the singularity-free solutions for anisotropic stellar structures in $f(R,\varphi )$ theory of gravity, where $R$ denotes the Ricci scalar and $\varphi$ represents the scalar field. For this purpose, we consider the spherically symmetric spacetime to discuss the stellar structures with anisotropic fluid. Moreover, the Einstein field equations are solved by using Chaplygin equation of state, and the Karori–Barua metric. To analyze the charged stellar structure, we use the matching conditions of spherically symmetric spacetime with the Reissner–Nordstrom exterior metric and develop some expressions for finding the unknown parameters. We further investigate the graphical behavior of energy density, pressure components, anisotropic component, equation of state parameters, equilibrium condition, stability analysis, adiabatic index and energy conditions. Conclusively, our considered stellar structures under observations are realistic, stable, and are free from any singularities.

The de Broglie gravitational waves are a solution of the linearized Einstein equations with properties that are absent in the standard gravity waves because they are also longitudinal waves and obey a dispersion relation that leads to an effective mass. Furthermore, they represent a classical realization of a form of dynamics, proposed for quantum particles by de Broglie in 1927. In this paper, we discuss the dynamics of a massive particle in presence of the de Broglie gravity wave. We will compute the analytical expression for the linear and angular momentum of the corpuscle. As an application, we will consider the case in which these oscillations of spacetime are associated to an electron travelling with a velocity equal to $1\%$ of the light speed and we will estimate the order of magnitude of the quantities involved. We will show that a nearby positron oscillates and radiates an energy of 1eV in $10^{-5}$s, an effect that is, in principle, measurable.

This paper is devoted to study FRW universe in the context of Chern–Simons corrected $f(R)$ gravity. In particular, the work provides the investigation of cosmological dynamics within modified gravity by assuming a suitable Hubble parameter that might result in a realistic bouncing universe. For this purpose, we consider a suitable Hubble parameter and examine the bouncing cosmology by assuming a well-known $f(R)$ gravity model. Further, we explore the behavior of energy density and pressure profiles by employing the chosen Hubble parameter. We obtain positive and increasing trends of energy density during the bouncing phase while the negative behavior of pressure in our work could potentially be associated with cosmic expansion. We have also studied the energy conditions and in our case NEC is not violated perhaps due to the reason that the equation of state parameter is not crossing the phantom divide. However, the SEC is violated justifying a successful bounce. Moreover, the validation of DEC and TEC suggests that the chosen model is well behaved in nature. The Hubble parameter passing through the bouncing point shows an increasing trend, indicating an expansion phase after the bounce. The equation of state parameter is negative after the bouncing spot, particularly around $\omega \approx -1$. This behavior justifies the current cosmic expansion. The deceleration parameter exhibits a negative behavior implies that the cosmological model demonstrates cosmic expansion. Thus all the results validate the existence of a bouncing universe with the chosen model in Chern–Simons corrected $f(R)$ gravity.