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Analytical methods provide crucial mathematical insights into the stable solitary waves hidden in nonlinear phenomena. The nonlinear Schrödinger (NLS) equation is one of the most important typical integrable soliton models. From a mathematical perspective, the essence of the celebrated derivative NLS (DNLS) equation’s difference from the classical NLS equation lies in its cubic potential being differentiated once by the spatial variable and multiplied by the imaginary unit, which leads to the former having some characteristics that the latter cannot have. This paper extends the DNLS equation to the fractional integrable case with conformable derivative operators, and uses Darboux transformations (DTs) and generalized DT (GDT) to solve it exactly. Specifically, Lax pairs generating the fractional DNLS equation are first given. Based on the given Lax pairs, then the n-fold DTs and GDT for the fractional DNLS equation are derived. Some special exact solutions of the fractional DNLS equation are further obtained by employing the derived n-fold DTs and GDT. Finally, several novel space–time structures and dynamical evolutions of the obtained exact solutions are analyzed. This paper reveals through the DT and GDT methods that the double power-law fractional orders in the exact solutions of the fractional DNLS equation can be used to dominate the variable velocity propagation and anomalous diffusion in fractional dimensional media at different geometric scales. [ABSTRACT FROM AUTHOR]

Smooth and discontinuous (SD) oscillators are the nonlinear models that will exhibit SD dynamics due to continuous variation of the smooth parameter. Kosambi–Cartan–Chern (KCC) theory is a differential geometric theory that describes the deviations from the entire trajectory of the variational equation to the nearby trajectory. This paper presents a completely new dynamical analysis of a type of SD oscillators with nonlinear damping based on the KCC theory. First, the paper gives five KCC geometrical invariants of SD oscillators in the smooth and non-smooth cases, respectively. The results show that the geometric quantities in the non-smooth case cannot be derived directly from the geometric quantities in the smooth case. Second, from these geometric quantities, KCC stability of SD oscillators trajectory at any point except x = 0 is analyzed. Lastly, numerical results show that in some regions that deviate from the equilibrium point of system, the system will exhibit complex and variable dynamical behavior due to small changes in parameters. This paper shows that the KCC theory is also a useful tool in the dynamical analysis of non-smooth systems. [ABSTRACT FROM AUTHOR]

This paper presents a methodical dynamical analysis of the Big Bang model, taking into account dark matter and an arbitrary form of dark energy. Nevertheless, why dynamic analysis? The primary advantage of the dynamical analysis approach is that it obviates the necessity to precisely solve the system for every individual dependent variable. Instead, it enables the prediction of the overall evolutions. In this regard, there are some powerful tools of non-dynamical systems (theorems, perturbation, etc.) which can help us a lot. The model under consideration is a nonlinear system with two dimensions (2D). In order to investigate this, we employ a sophisticated form of nonlinear dynamical systems theory in our research. We have delved into the full potential of nonlinear dynamical system theory known until now in our work. This analysis has produced very interesting solutions, which are in quite a contrast with the linear analysis approach. The stability of the system is considered at length, and the corresponding evolutions of the universe are also discussed consequently. A handful number of figures are given to visualize the behavior of the evolutions. The plots that are presented here are vector field plots and a new plotting technique initiated by us and used in our earlier papers. Interestingly, our work indicates the universe might resemble “phantom” evolution. Also, among the fixed points of our model, one is able to escape the singular situation called “Big Rip”. [ABSTRACT FROM AUTHOR]

In this paper, we investigate in this paper the Type IV singular bouncing in the framework of f (R ,) theory of gravity where R and mean the curvature scalar and the Gauss–Bonnet invariant, respectively. Cosmological f (R ,) models constrained by the slow-roll evolution is reconstructed and their explicit forms are provided near the bounce and far away from it. One obtains finally two models whose stability is numerically analyzed in this work. Our results show that the stability of the reconstructed models is very affected by their parameters. The model far from the singularity recovers stability quickly than the model near the singularity. [ABSTRACT FROM AUTHOR]

This paper presents an analytical study of the behavior of radial free-geodesics in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime within the Lambda Cold Dark Matter (Λ CDM) model. Using the radial free motion solutions, we provide two methods for characterizing the geodesics and defines a general formula that encapsulates all possible solutions, determined by two initial conditions. We show that the past light cone, event horizon, and particle horizon, can be considered as special cases of this overarching formula. Furthermore, the paper explores the free geodesics within the currently accepted cosmological model based on the recent Planck results, thoroughly examining the various possible geodesic scenarios. [ABSTRACT FROM AUTHOR]

In previous works, we have proven that there are local tetrads in four-dimensional curved Lorentzian spacetimes that can be written in terms of two kinds of local structures, the skeletons and the gauge vectors. These tetrads diagonalize locally and covariantly the stress–energy tensors for systems of differential equations of the Einstein–Maxwell kind in the Abelian electromagnetic case, or of the Einstein–Maxwell–Yang-Mills kind when non-Abelian Yang–Mills fields are included, along with suitable Yang–Mills stress–energy tensors. Under local Lorentz transformations, these new tetrads conserve their skeleton-gauge vector structure. In this short paper, we will prove that given any general unit orthogonal tetrad in spacetime, we will be able to construct a new tetrad in the skeleton-gauge vector form. We will prove a theorem stating that the original orthonormal tetrad can be constructed or reexpressed with this same local tetrad skeleton-gauge vector structures. The theorems proved in this paper will enable the demonstration of new results in group isomorphism theorems in the future. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of conformal metric deformations in the quasi-radial coordinate parametrizing the three-sphere in the conformally compactified Minkowski spacetime S1 × S3. Prior to reduction of the associated Laplace–Beltrami operators to a Schrödinger form, a corresponding class of exactly solvable potentials (each one containing a scalar and a gradient term) is found. In particular, the scalar piece of these potentials can be exactly or quasi-exactly solvable, and among them we find the finite range confining trigonometric potentials of Pöschl–Teller, Scarf and Rosen–Morse. As an application of the results developed in the paper, the large compactification radius limit of the interaction described by some of these potentials is studied, and this regime is shown to be relevant to a quantum mechanical quark deconfinement mechanism. [ABSTRACT FROM AUTHOR]

This paper considers the possibility that abstract thinking and advanced synthesis skills might encourage extraterrestrial civilizations to accept communication with mankind on Earth. For this purpose, a notation not relying upon the use of alphabet and numbers is proposed, in order to denote just some basic geometric structures of current physical theories: vector fields, 1-form fields, and tensor fields of arbitrary order. An advanced civilization might appreciate the way here proposed to achieve a concise description of electromagnetism and general relativity, and hence it might accept the challenge of responding to our signals. The abstract symbols introduced in this paper to describe the basic structures of physical theories are encoded into black and white bitmap images that can be easily converted into short bit sequences and modulated on a carrier wave for radio transmission. [ABSTRACT FROM AUTHOR]

This paper investigates discrete symmetries for dyon and the invariance of Maxwell's field equations in the macroscopic media (material medium). Using advanced mathematical approaches, the paper derived electromagnetic duality and a unique form of Poynting theorem for dyon in macroscopic media. Here, we demonstrate that the combination of parity (P) , charge conjugation (C) , and time reversal (T) symmetry: CPT , is an exact symmetry for dyon in macroscopic media. Furthermore, a comprehensive analysis of the electromagnetic wave equation for dyons in conducting media is also derived. These findings contribute significantly to the understanding of dyon behavior in electromagnetic fields. [ABSTRACT FROM AUTHOR]

The finding of new integrable coupling systems has become an important area of research in mathematical physics and their study will aid in the classification of multi-component integrable systems. A basic method for generating integrable coupling systems is algebraic expansion, for example, the Frobenius algebra, the Lie algebra, the superalgebra, and so on. In this paper, we introduce a Frobenius Boussinesq equation based on the Frobenius algebra, and then we present a Lax pair of it. It follows that we give a Bäcklund transformation of the Frobenius Boussinesq equation. Furthermore, the lattice equation of the Frobenius Boussinesq equation is presented by using three Bäcklund transformations, and then obtain the exact solutions. Additionally, we obtain the conservation laws of the Frobenius Boussinesq equation via the Bäcklund transformation. Strongly coupled and weakly coupled systems physically represent strong and weak interactions, respectively. In this paper, we introduce a weakly coupled Degasperis–Procesi (DP) equation, and construct a Lax pair of it. In addition, the Bäcklund transformation and superposition principle are applied to investigate the weakly coupled DP equation. We also obtain the conservation laws of the weakly coupled DP equation. Then, we introduce a strongly coupled DP equation, and use the same method to study the strongly coupled DP equation. The exact solutions of these two equations are obtained. Moreover, we introduce a Z n -DP equation. Considering the superposition principle, we obtain the solution of an associated Z n -DP equation by using Bäcklund transformations. These new multi-component integrable systems can enrich the existing integrable models and possibly describe new nonlinear phenomena. [ABSTRACT FROM AUTHOR]

In this paper, it has been proven that locally the inertial frames and gauge states of the electromagnetic field are equivalent. This proof is valid for Einstein–Maxwell theories in four-dimensional Lorentzian spacetimes. Theorems proved in a previous paper will be used. These theorems state that locally the group of electromagnetic gauge transformations is isomorphic to the local group of Lorentz transformations of a special set of tetrad vectors. The tetrad that locally and covariantly diagonalizes any non-null electromagnetic stress–energy tensor. There are in total two isomorphisms, one for each orthogonal plane of stress–energy eigenvectors. We discuss the opposite problem in this paper. What happens with local electromagnetic gauge when the test object under study is boosted by any mechanical means? We will prove that boosting matter is indistinguishable from introducing an appropriate local electromagnetic gauge transformation. [ABSTRACT FROM AUTHOR]

The primary objective of this paper is to examine singularity-free solutions within the framework of anisotropic solutions for the Chaplygin equation of state in f (R , ϕ , X) modified gravity theory. Herein, R signifies the Ricci scalar, ϕ denotes the scalar field, and X represents the kinetic term associated with ϕ. The investigation employs the Krori–Barua metric to explore the characteristics of an anisotropic compact star. In the course of our analysis, we specifically consider observational data about three distinct stellar structures: Her X-I, LMC X-4, and 4U 1538-52. Our inquiry extends to the graphical examination of various physical parameters, encompassing energy density, pressure components, anisotropic components, equation of state parameters, equilibrium conditions, stability analysis, adiabatic index, and energy conditions. Furthermore, we delve into the intricacies of the mass-radius function, compactness factor, and surface redshift–integral features of charged compact stars. The culmination of our findings suggests that the f (R , ϕ , X) theory of gravity when subjected to observational scrutiny, manifests as realistic, stable, and devoid of singularities. [ABSTRACT FROM AUTHOR]

Monounary algebras are the most simple type of an algebraic structure. Oriented graphs with one outgoing arrow from every vertex represent them. The aim of this paper is to point out the interdisciplinary relationships concerning this structure. Bernoulli shift is a paradigmatic mapping in dynamical systems. It is also called dyadic, bit shift, doubling or sawtooth. We offer a look at the properties of this mapping via monounary algebras. [ABSTRACT FROM AUTHOR]

In this paper, we have computed the spectrum and the q -index of the super q -deformed Ginsparg–Wilson Dirac operator in the different cases (fuzzy, non-fuzzy, gauged, and non-gauged) on the superquantum fuzzy two-sphere S q μ (2 | 2) . We also presented the appropriate spin structure that this operator acts on the superquantum (Dirac) spinor bundle. Finally, it was shown that in the non-quantum limit, when q tends to 1, in each case, there is a correct commutative limit for the spectrum and the q -index. [ABSTRACT FROM AUTHOR]

The goal of this paper is to analyze sharp-type inequalities including the scalar and Ricci curvatures of bi-slant Riemannian submersions in complex space forms. Then, for bi-slant Riemannian submersion between a complex space form and a Riemannian manifold, we give inequalities involving the Casorati curvature of the space ker φ ∗ . Also, we mention some examples. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the conditions for mapping the geometric description of the kinematics of particles that probe a given Hamiltonian in phase space to a description in terms of Finsler geometry (and vice-versa). [ABSTRACT FROM AUTHOR]

In this paper, we study the tunneling radiation from a charged-accelerating AdS black hole with gauge potential under the impact of quantum gravity. Using the semi-classical phenomenon known as the Hamilton–Jacobi ansatz, it is studied that tunneling radiation occurs via the horizon of a black hole and also employs the Lagrangian equation using the generalized uncertainty principle. Furthermore, we investigate the impact of charge, gauge potential, and first order correction parameters on the temperature as well as the stable and unstable states of the black hole. We also compute thermodynamic properties such as entropy, internal energy, Helmholtz free energy, enthalpy, specific heat, and Gibbs free energy under the impact of the correction parameter for the black hole. We calculate the logarithmic modification terms for entropy around the equilibrium state to analyze the impacts of logarithmic correction. In the presence of the correction terms, we also check the validity of the thermodynamics. It examines the graphical representation of the influence of logarithmic correction on the thermodynamic properties of black hole stability as well as charged, accelerating, and gauge potential parameters. [ABSTRACT FROM AUTHOR]

It is known that the Frenet–Serret apparatus of a space curve in three-dimensional Euclidean space determines the local geometry of curves. In particular, the Frenet–Serret apparatus specifies important geometric invariants, including the curvature and the torsion of a curve. It is also acknowledged in quantum information science that low complexity and high efficiency are essential features to achieve when cleverly manipulating quantum states that encode quantum information about a physical system. In this paper, we propose a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by dynamically evolving state vectors. Specifically, we propose a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced by a parallel-transported pure quantum state evolving unitarily under a stationary Hamiltonian specifying the Schrödinger equation. Our proposed constant curvature coefficient is given by the magnitude squared of the covariant derivative of the tangent vector | T 〉 to the state vector | Ψ 〉 and represents a useful measure of the bending of the quantum curve. Our proposed constant torsion coefficient, instead, is defined in terms of the magnitude squared of the projection of the covariant derivative of the tangent vector | T 〉 , orthogonal to both | T 〉 and | Ψ 〉. The torsion coefficient provides a convenient measure of the twisting of the quantum curve. Remarkably, we show that our proposed curvature and torsion coefficients coincide with those existing in the literature, although introduced in a completely different manner. Interestingly, not only we establish that zero curvature corresponds to unit geodesic efficiency during the quantum transportation in projective Hilbert space, but we also find that the concepts of curvature and torsion help enlighten the statistical structure of quantum theory. Indeed, while the former concept can be essentially defined in terms of the concept of kurtosis, the positivity of the latter can be regarded as a restatement of the well-known Pearson inequality that involves both the concepts of kurtosis and skewness in mathematical statistics. Finally, not only do we present illustrative examples with nonzero curvature for single-qubit time-independent Hamiltonian evolutions for which it is impossible to generate torsion, but we also discuss physical applications extended to two-qubit stationary Hamiltonians that generate curves with both nonzero curvature and nonvanishing torsion traced by quantum states with different degrees of entanglement, ranging from separable states to maximally entangled Bell states. In the Appendix C, we examine the different curvature and torsion characteristics of the three qubit | GHZ 〉 and | W 〉 states under evolution by a quantum Heisenberg Hamiltonian. [ABSTRACT FROM AUTHOR]

In this research paper, we determine the nature of conformal η -Ricci–Bourguignon soliton on a general relativistic spacetime with torse forming potential vector field. Besides this, we evaluate a specific situation of the soliton when the spacetime admitting semi-symmetric energy–momentum tensor with respect to conformal η -Ricci–Bourguignon soliton, whose potential vector field is torse-forming. Next, we explore some characteristics of curvature on a spacetime that admits conformal η -Ricci–Bourguignon soliton. In addition, we turn up some physical perception of dust fluid, dark fluid and radiation era in a general relativistic spacetime in terms of conformal η -Ricci–Bourguignon soliton. Finally, we examine necessary and sufficient conditions for a 1-form η , which is the g -dual of the vector field ξ on general relativistic spacetime to be a solution of the Schrödinger–Ricci equation. [ABSTRACT FROM AUTHOR]

In this paper, we present a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by state vectors evolving under nonstationary Hamiltonians. Specifically, relying on the existing geometric viewpoint for stationary Hamiltonians, we discuss the generalization of our theoretical construct to time-dependent quantum-mechanical scenarios where both time-varying curvature and torsion coefficients play a key role. Specifically, we present a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced out by a parallel-transported pure quantum state evolving unitarily under a time-dependent Hamiltonian specifying the Schrödinger evolution equation. The time-varying curvature coefficient is specified by the magnitude squared of the covariant derivative of the tangent vector | T 〉 to the state vector | Ψ 〉 and measures the bending of the quantum curve. The time-varying torsion coefficient, instead, is given by the magnitude squared of the projection of the covariant derivative of the tangent vector | T 〉 to the state vector | Ψ 〉 , orthogonal to | T 〉 and | Ψ 〉 and, in addition, measures the twisting of the quantum curve. We find that the time-varying setting exhibits a richer structure from a statistical standpoint. For instance, unlike the time-independent configuration, we find that the notion of generalized variance enters nontrivially in the definition of the torsion of a curve traced out by a quantum state evolving under a nonstationary Hamiltonian. To physically illustrate the significance of our construct, we apply it to an exactly soluble time-dependent two-state Rabi problem specified by a sinusoidal oscillating time-dependent potential. In this context, we show that the analytical expressions for the curvature and torsion coefficients are completely described by only two real three-dimensional vectors, the Bloch vector that specifies the quantum system and the externally applied time-varying magnetic field. Although we show that the torsion is identically zero for an arbitrary time-dependent single-qubit Hamiltonian evolution, we study the temporal behavior of the curvature coefficient in different dynamical scenarios, including off-resonance and on-resonance regimes and, in addition, strong and weak driving configurations. While our formalism applies to pure quantum states in arbitrary dimensions, the analytic derivation of associated curvatures and orbit simulations can become quite involved as the dimension increases. Thus, finally we briefly comment on the possibility of applying our geometric formalism to higher-dimensional qudit systems that evolve unitarily under a general nonstationary Hamiltonian. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the geometric phase (GP) of two-mode entangled squeezed-coherent states (ESCSs), undergoing unitary cyclic evolution. Results show that increasing the squeezing parameter of either mode of the balanced ESCS compresses the GP elliptically with respect to the coherence parameter of the corresponding mode. While in the case of unbalanced ESCS, the GP is compressed hyperbolically by increasing the squeezing parameters of the either mode. By generalizing the approach to higher constituting-state dimensions, it is found that the GPs of both balanced and unbalanced ESCSs, increase for a specific value of the coherence parameter. By analyzing the states through the Schmidt decomposition method, we find that, locally, the balanced and unbalanced ESCSs are unitarily equivalent. Finally, based on the interferometry technique, we suggest a theoretical scheme for the physical generation of ESCSs. [ABSTRACT FROM AUTHOR]

The Schrödinger–Hirota equation is one of the most important models of contemporary physics which is popular throughout the broad fields of fluid movement as well as in the study of thick-water crests, liquid science, refractive optical components and so on. In this paper, we utilize the Hirota bilinear technique and the unified technique to attain various soliton solutions of the governing model analytically. These approaches are robust, powerful and unique also have many applications in different fields of mathematical physics. The solutions attained from these techniques are highly valuable and useful in various fields of sciences specially in the transmissions of optical fibers, also they give different behaviors including V-shaped and periodic soliton solution behavior. Further, the approaches applied here are not applied in this model previously. Therefore, ours is a new work, which summarizes its novelty. The 3D, 2D and contour plots are included to grasp the understanding of solutions' behavior. These findings are valuable in electronic communications such as elliptical circuits and in investigation of solitude controlling. [ABSTRACT FROM AUTHOR]

In this paper, we review a recently offered notion of quasi-static evolution of the axial self-gravitating structures at large scales and the criterium to characterize the corresponding evolutionary aspects under the influence of strong curvature regimes. In doing so, we examine the axial source's dynamic and quasi-static behavior within the parameters of various modified gravity theories. We address the formalism of these notions and their possible implications in studying the dissipative and anisotropic configuration. We initiate by considering higher-order curvature gravity. The Palatini formalism of f (R) gravity is also taken into consideration to analyze the behavior of the kinematical as well as the dynamical variables of the proposed problem. The set of invariant velocities is defined to comprehend the concept of quasi-static approximation that enhances the stability of the system in contrast to the dynamic mode. It is identified that vorticity and distinct versions of the structure scalars Y I , Y II and Y KL play an important role in revealing the significant effects of a fluid's anisotropy. As another example of evolution, we check the influence of Palatini-based factors on the shearing motion of the object. A comparison-based study of the physical nature of distinct curvature factors on the propagation of the axial source is exhibited. This provides the intriguing platform to grasp the notion of quasi-static evolution together with the distinct curvature factors at current time scenario. The importance of slowly evolving axially symmetric regimes will be addressed through the distinct modified gravitational context. Finally, we share a list of queries that, we believe, deserve to be addressed in the near future. [ABSTRACT FROM AUTHOR]

The matter–anti-matter asymmetry in the early Universe’s history is explained theoretically by the baryogenesis. It is well known that modified gravity theories are highly effective in explaining the Universe’s current accelerated state. In this paper, we examine the gravitational baryogenesis for f(Q,C) gravity, where Q is the non-metricity scalar and C is the boundary term. To perform the baryogenesis, we assume linear, nonlinear and logarithmic forms of f(Q,C). We evaluate the baryon-to-entropy ratio for our models by assuming the power law form of the scale factor a(t) = a0tδ. We also investigate the generalized baryogenesis for our model by assuming the interaction term ∂μ(Q + C). We constrain the model parameters by comparing with the observational value ηB s = 9.42 × 10−11. Our derived models are physically viable. [ABSTRACT FROM AUTHOR]

This paper examines the viable characteristics of anisotropic compact stars in f(ℜ,T2) theory (ℜ is the Ricci scalar and T2 = T αβTαβ). In this perspective, we use Tolman–Kuchowicz solutions (μ = wr2 + 2ln z and ν =ln(1 + xr2 + yr4)) to examine the configurations of static spherically symmetric structures. The unknown constants are found by the first fundamental form of Darmois junction conditions. We analyze the behavior of fluid parameters in the interior of 4U 1538-52, PSRJ 1614-220, EXO 1785-248 and SAXJ 1808.4-3658 compact stars correspond to different models of this theory. Furthermore, the stability of the proposed compact stellar objects is examined through sound speed and adiabatic index methods. The satisfaction of requisite conditions ensures that stable compact objects exist in this framework. [ABSTRACT FROM AUTHOR]

In recent decades, nano/microelectromechanical systems (N/MEMS) have garnered significant attention due to their appealing characteristics, such as compact size, batch fabrication capabilities, high reliability and low power consumption. However, these vibratory systems often present challenges, including zero conditions at the initial time, involving zero velocity and zero displacement, which complicates the solution process. Nonetheless, the theory of geometric potential offers insights into various phenomena in nanoscience and nanotechnology. In this paper, we implement the theory of geometric potential to develop an N/MEMS model. We then analyze the periodicity property of the nonlinear system using a novel method based on Sturm’s algorithm. Our analysis reveals that the model with zero initial conditions exhibits periodic solution under specific conditions on lumped parameter. Finally, we validate our findings by comparing them with numerically achieved results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new convexity notion for inter-valued functions, known as Geometrically–Arithmetically Cr-h-convex functions (abbreviated as GA-Cr-h-CFs) and explore its properties. The family of GA-Cr-h-CFs simultaneously covers the family of GA-CFs, GA-h-CFs and GA-Cr-CFs. On the other hand, we demonstrate its equivalence with convex functions (CFs), h-CFs, Cr-CFs and Cr-h-CFs via exponential function. We also investigate necessary and sufficient conditions for GA-Cr-h-CFs via two corresponding real-valued GA-h-CFs. Due to significance and applications of mathematical inequalities, we apply our findings and propose several inequalities such as Jensen–Mercer inequality (JMI), Hermite–Hadamard inequality (HHI) and weighted Hermite–Hadamard-type inequalities (wHHIs) for GA-Cr-h-CFs. Through our results, we re-capture many known results and inequalities for subclasses of GA-Cr-h-CFs studied in the recent literature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate conformal η-Ricci–Yamabe soliton on semiconformally flat Kählerian Norden spacetime in conjunction with the Kählerian Norden torse-forming vector field. Furthermore, we examine various physical aspects of such soliton on special fluid spacetime, such as dust fluid, dark fluid, radiation era, viscous fluid, and heat flux. In addition, we light up the harmonic features of conformal η-Ricci-Yamabe soliton on semiconformally flat Kählerian Norden spacetime. Finally, we also deduce the necessary and sufficient conditions for a 1-form η, which is the g-dual of the vector field ξ on such a spacetime, to be a solution of the Schrödinger-Ricci equation. [ABSTRACT FROM AUTHOR]

In this paper, we mainly make research on whether fractal characteristics of an object with a fractal curve shape will keep invariable under being subjected to horizontal linear stretching. For two continuous functions f(x) and g(x), it has been proven that the graph of f[g(x)] has the same fractal dimensions with the graph of f(x) when g(x) is a linear function. Some examples have also been provided to corroborate our theoretical results. This work may contribute to the dimensional theory of fractal curves and have practical application significance in physics. [ABSTRACT FROM AUTHOR]

In this paper, we present the Noether symmetries of locally rotationally symmetric Bianchi-type I (LRS BI), an anisotropic model, in the context of the teleparallel gravity. We study a certain modified teleparallel theory based on the action that, in particular, contains a coupling between the scalar field and field strength (magnetism part). We derive the symmetry generators and show that, by means of cyclic variables approach, one can not obtain a suitable solution for field equations. Hence by the use of beyond Noether symmetry (B.N.S.) approach, we solve the equations which carry Noether currents as well. By data analysis of the obtained results, compatible results with observational data at the last half of the age of universe which is accelerating are demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, the discrete octonion linear canonical transform (DOCLCT) is presented. According to the definition of DOCLCT, its shift transform and modulation transform are explored. In addition, based on a new convolution operator, we obtain the convolution theorem of DOCLCT. The DOCLCT can be derived by the three-dimensional (3D) linear canonical transform. So, the fast algorithm of 3D DOCLCT is discussed. Finally, Heisenberg’s uncertainty principle associated with DOCLCT is established. [ABSTRACT FROM AUTHOR]

The primary objective of this study is to conduct a thorough examination of relativistic structures within the framework of f(ℛ,풯 ) gravity, where ℛ is the Ricci scalar and 풯 is the trace of the energy–momentum tensor. We investigate the emerging characteristics of compact stars, focusing on the ℛ + 2ξ풯 model, where ξ is the coupling constant. In the initial sections of the paper, we concentrate on the examination of exact interior solutions involving perfect fluid. With this aim, we introduce the metric coefficient L = S(1 + 2ar2)d/2, where a and S are arbitrary constants to be computed from the matching conditions and d is a positive odd integer. It is worth noticing that we select a group of 10 significant compact stars from recent studies, namely, Vela X − 1, EXO 1785 − 248, 4U1820 − 30, SMCX − 4, HerX − 1, PSR J1614 − 2230, PSRJ1903 + 327, CenX − 3, 4U1538 − 52 and LMCX − 4. To investigate the viability of our model, we conduct various checks, including the analysis of energy density and pressure components, equilibrium, and energy conditions, stability analysis and the adiabatic index. An important part of this work provides the slowly rotating property of stars, accompanied by the derivation of the moment of inertia. The relationship of mass, energy density, radius and moment of inertia for stellar objects are observed. Our findings demonstrate that obtained results are physically acceptable and consistent with our considered model. [ABSTRACT FROM AUTHOR]

This paper is devoted to analyzing a new model of a coupled Langevin system with fractional operators under nonlocal antiperiodic integral boundary conditions. This model involves nonlinear Langevin fractional equations with Caputo–Hadamard and Caputo fractional operators. Also, the existence and uniqueness of solutions to the suggested model have been investigated by the fixed-point technique. Moreover, the Hyers–Ulam stability of the solutions has been discussed. Finally, we provide an illustrative example to support the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we establish a connection between Sisyphus dynamics and the Liénard-II equation through branched Hamiltonians. Sisyphus dynamics stem from a higher-order Lagrangian. Surprisingly, when expressed in terms of velocity, the Sisyphus dynamical equations align closely with the Liénard-II equation. Sisyphus dynamics introduces velocity-dependent “mass functions”, a departure from conventional position-dependent mass, potentially linked to cosmological time crystals. Additionally, we demonstrate that spontaneously broken time translational symmetry results in a deformed symplectic structure, resembling the classical counterpart of the Generalized Uncertainty Principle (GUP). [ABSTRACT FROM AUTHOR]

Observational evidence revealed that in the composition of the Universe, the dark energy is in heap proportion which is mainly responsible for the accelerated expansion of the Universe. The astrophysicists hypothesized that every astrophysical object is likely interact with the dark energy Sakti and Sulaksono [Phys. Rev. D 103 (2021) 084042]. Therefore, researchers are intended to study the astrophysical objects with dark energy interaction. In this paper, we proposed a dark energy stars (composed of with dark matter and ordinary matter) model in the Rastall theory of gravity. The Rastall field equations are obtained in the Tolman–Kuchowicz-type metric. To solve the field equations, the arbitrary constants involved in the field equations (due to Tolman–Kuchowicz ansatz) are obtained by matching the interior geometry with the exterior Schwarzschild geometry. The obtained solution is tested physically by computing some analytical results and plotting graphs of different physical parameters like pressure, density for ordinary matter, density for dark matter, mass function, compactness and surface redshift. Stability of the model is also analyzed by different tests like velocity of sound, adiabatic index and TOV equations. The influence of the Rastall parameter on the model has been studied by plotting graphs and computing numerical values of model’s physical parameters for different values of the Rastall parameter. We infer that our propounded model fulfills all the necessary requirements for a physically plausible model. [ABSTRACT FROM AUTHOR]

This paper considers the only sectors to constitute the present universe as the dark matter and dark energy. The proposed new agegraphic dark energy model studies the gradual transition from matter to dark energy in sequential order, including the current dominance of the matter sector by dark energy. The model utilizes concepts of Tsallis entropy and the Karolyhazy relation with conformal time η as the time scale. Various evolutionary aspects of the universe are characterized by Tsallis parameter δ and the model constant c. Expressions for dynamic behavior of dark energy, as a differential equation, equation of state and deceleration parameters are obtained to describe the thermal history of universe evolution. Also, the stability of the model is analyzed through squared sound speed parameter. The analysis is made by considering an interaction as well as independence among the constituent sectors of the universe. [ABSTRACT FROM AUTHOR]

This paper is an investigation of dark energy cosmological models in non-coincident gauge formulation of non-metricity gravity with boundary term. We have considered an arbitrary function f(Q,C) = Q + λCm, where Q is the non-metricity scalar, C is the boundary term derived by C = R̈ − Q, and λ,m are the model parameters, to obtain the modified field equations from action. We have parameterized the Hubble function as H(a) = k0(a(t)−n + k 1) with n,k0,k1 are arbitrary constants and a(t) is the scale-factor depending upon cosmic time. We have compared this Hubble function with H(z) datasets and obtained best fit values of model parameters using likelihood analysis. Using these best fit values of model parameters, we have done our result analysis and discussion with cosmological parameters viz effective equation of state parameter, energy density, energy conditions, deceleration parameter, om diagnostic analysis and age of the universe. We have found a transit phase universe model with effective EoS parameter − 1.18 < ωeff < −0.2 over redshift − 1 < z < 3. [ABSTRACT FROM AUTHOR]

The general relativity unification and quantum theory is a significant open problem in theoretical physics. This problem arises from the fact that these two fundamental theories, which describe gravity and the behavior of particles at the microscopic level, respectively, are currently incompatible. The unification of these theories is crucial for a complete comprehension of the fundamental forces and the nature of the universe. In this regard, the quantum properties of a Black Hole result in fundamental importance. By analyzing such properties in quantum field theory, in the first step, the gravity enters as a classical background. In semi-classical approximation, Black Holes will emit Hawking radiation with an almost thermal spectrum, while Black Hole's entropy is proportional to the Black Hole's horizon. Besides, Hawking's temperature and Black Hole entropy should follow the first law of Black Hole thermodynamics. Also, Jacobson [Thermodynamics of spacetime: The Einstein equation of state, Phys. Rev. Lett.75 (1995) 1260, doi:10.1103/PhysRevLett.75.1260] showed shown that there is a connection between Black Hole thermodynamics and Einstein's equation that opens the root of a potential thermodynamic nature of gravity. This issue opened a new impressive research framework in which the Einstein field equation can be expressed as a form of the first law of thermodynamics and vice versa. In this study, it is assumed that the universe has a fractal structure. Accordingly, modified Friedmann's equations and the Black Holes thermodynamics in a fractal universe have been examined. The fractal framework shows what features and changes occur in the description of the universe, particularly in studying the thermodynamics of a Black Hole. However, the paper strategy is organized as follows: in the beginning, we consider the first thermodynamic law in a fractal universe. Then, we investigate the Friedmann equation of the fractal universe in the form of the entropy balance, this means d Q = T h d S h , where d Q and T h are the thermal energy and horizon temperature. We consider the entropy S h have two terms; (1) obeys the usual area law and (2) the entropy production term due to the non-equilibrium thermodynamics of a fractal universe. Therefore, in a fractal universe, a term with non-equilibrium thermodynamics of spacetime may be needed. Also, we study the generalized second law of thermodynamics in a fractal universe. When the temperature of the apparent horizon and the temperature of the matter fields inside the horizon are equal, i.e. T = T h , the second law of generalized thermodynamics can be obtained according to the state parameter range equation, which is consistent with the recent observations. Finally, in Sec. 6, based on the mathematical calculations, we study the various cosmological parameters such as the Hubble parameter, scale factor, deceleration parameter and equation of state parameter. [ABSTRACT FROM AUTHOR]

A generalized Robertson–Walker spacetime is not, in general, a perfect fluid spacetime and the converse is not, in general, true. In this paper, we show that if a perfect fluid spacetime admits an η – ρ -Einstein soliton, then the integral curves generated by the velocity vector field u are geodesics and the acceleration vector vanishes. Also, we show that if a perfect fluid spacetime with Killing velocity vector field admits a gradient η – ρ -Einstein soliton, then the spacetime represents either dark matter era or, the acceleration vector vanishes. Next, we show that if a generalized Robertson–Walker spacetime admits an η – ρ -Einstein soliton, then it becomes a perfect fluid spacetime. Finally, we prove that in a dark matter fluid with vanishing vorticity satisfying gradient η – ρ -Einstein soliton in f (ℛ) -gravity with constant Ricci scalar, either the energy density and isotropic pressure are constant or, the potential function ψ remains invariant under the velocity vector u. Also, for two models f (ℛ) = e α ℛ + α log ℛ and f (ℛ) = ℛ n (α = constant and ℛ is the Ricci scalar of the spacetime), various energy conditions in terms of the Ricci scalar are examined and state that the Universe is in an accelerating phase and satisfies the weak, null and dominant energy conditions, but violate the strong energy condition. [ABSTRACT FROM AUTHOR]

In this paper, we investigate null Cartan geodesic isophote curves in the Minkowski 3 -space, and give examples where such curves actually exist. By categorizing the types of light vectors, we characterize different types of null Cartan geodesic isophote curves. Moreover, we present the relationship between null Cartan geodesic isophote curves and other special curves. [ABSTRACT FROM AUTHOR]

Differentiation of the scalar Feynman propagator with respect to the spacetime coordinates yields the metric on the background spacetime that the scalar particle propagates in. Now Feynman propagators can be modified in order to include quantum-gravity corrections as induced by a zero-point length L > 0. These corrections cause the length element s 2 to be replaced with s 2 + 4 L 2 within the Feynman propagator. In this paper, we compute the metrics derived from both the quantum-gravity free propagators and from their quantum-gravity corrected counterparts. We verify that the latter propagators yield the same spacetime metrics as the former, provided one measures distances greater than the quantum of length L. We perform this analysis in the case of the background spacetime ℝ D in the Euclidean sector. [ABSTRACT FROM AUTHOR]

In this paper, we study the cosmic dynamics of varying vacuum models where the dark matter interacts with the vacuum energy. We consider the homogeneous and isotropic spacetime with spatial curvature and apply the dynamical system technique to the varying vacuum models by specifying the form of energy exchange rate (Q) between the dark energy and dark matter. Further, we utilize the cosmographic parameters and statefinder parameters in the terms of dynamical variables of the cosmological dynamical system to explore the cosmic dynamics of the universe. The Milne universe solution exists as a consequence of spatially curved geometry in the model. The models also yield radiation- matter- and dark energy-dominated phases in order and thus explain the late-time accelerated expansion of the universe. The strength of interaction terms will affect the existence of cosmological phases in the model but there will always be an attractor corresponding to the accelerating universe. We numerically solve the system to illustrate the evolution of cosmological quantities and dynamical variables in the models. The role of curvature is visible during the transition from the decelerated phase into the accelerating phase. The numerical solutions affirm that the cosmological parameters in the models are consistent with their corresponding observational values. [ABSTRACT FROM AUTHOR]

A set of position-dependent noncommutative algebra in two dimension (2D) that describes the space near the Planck scale had been introduced [J. Phys. A: Math. Theor. 53 (2020) 115303]. This algebra predicted the existence of maximal length of graviton measurable at low energy. From this algebra, we deduce in the present paper, a new noncommutative algebra that is compatible with the deformed algebra proposed by Costa Filho et al. [Phys. Rev. A84 (2011) 050102] to describe the Position-Dependent Mass (PDM) system in 1D. To this aim, we derive from the momentum operators, the Schrödinger-like equation which describes PDM system in null quantum well potential. The spectrum of this system is asymetrically deformed and exhibits different behaviours from the one obtained by Costa Filho et al. Thus, we observe that by increasing the PDM, the energy decreases and this decrease is more pronounced as the quantum number increases. Finally, we evaluate the thermodynamic quantities within the canonical ensemble and we show that these results are consistent with the ones recently obtained by Bensalem and Bouaziz [Phys. A Stat. Mech. Appl.523 (2019) 583–592]. [ABSTRACT FROM AUTHOR]

In this paper, we perform a complete non-relativistic study of the improved class of inversely quadratic Yukawa plus Hulthén potential (ICIQYHP) model in the context of three-dimensional non-relativistic non-commutative quantum phase-space (3D-NRNCPS) symmetries impacted by perturbed spin–orbit interaction and the external magnetic fields for the homogeneous (N2 and O2) and heterogeneous (CO and NO) diatomic molecules and the heavy meson systems, such as charmonium (cc) and bottomonium (bb) using generalized Bopp's shifts method and standard perturbation theory with the Greene–Aldrich approximation to the centrifugal barrier. The new non-relativistic energy equation and eigenfunction for the ICIQYHP in the presence of deformation phase–space are obtained to be sensitive to the atomic quantum numbers (j , l , s , and m), the mixed potential depths ( V 0 1 , V 2 1 , V 1 1 and V 3 1 ), the screening parameter δ 0 , and non-commutativity parameters (Φ / η ¯ , χ / χ ¯ and ζ / ζ ¯). The critical particular cases in 3D-NRNCPS symmetries have been obtained by adjusting the parameters of the ICIQYHP, such as the improved Hulthén potential, the improved Coulomb potential, and the improved inversely quadratic Yukawa potential. We have also studied the spin-averaged mass spectra of the heavy mesons and the thermo-magnetic properties under the class of inversely quadratic Yukawa plus Hulthén potential model in 3D-NRQM and 3D-NRNCPS symmetries. This research can potentially be applied to atomic, condensed matter, nuclear, molecular physics, and chemical physics. [ABSTRACT FROM AUTHOR]

In this paper, we propose a specialized parameterization for the Hubble parameter, inspired by Λ CDM cosmology, to investigate the cosmic expansion history of the Universe. This parameterization is employed to analyze the universe's late-time behavior within the context of Q n gravity, where Q represents non-metricity. By using data from 57 Hubble data points, 1048 supernova (SNe) data points, and six Baryon Acoustic Oscillation (BAO) data points, we determine the optimal values for the model parameters. Additionally, we explore three distinct cosmological models based on the parameter n , specifically when it takes on the values of 0. 5 5 , 1. 5 and 2. 0. The results of our analysis indicate that our proposed parameterization, along with the associated models for different values of n , predicts an accelerated cosmic expansion phase. [ABSTRACT FROM AUTHOR]

In this paper, the coupled system nonlinear (2 + 1)-dim Broer–Kaup–Kupershmit (BKK) equation under consideration is based on extension of modified rational expansion method. The various kinds of multiple soliton solutions named anti-kink soliton, traveling wave solutions, periodic solution, dark soliton, kink soliton, bright soliton, anti-kink bright solitons, kink bright solitons for nonlinear BKK system are successfully constructed under symbolic computation Mathematica. The calculated results are very interesting, different and novel which have not been investigated in past literature. The graphical demonstration of constructed solutions show by contour, 2D and 3D shape by using computer software Mathematica. The constructed multiple soliton solutions prove that EMRE approach is very straightforward, efficient, reliable and powerful for the investigation of other nonlinear partial differential equations. The investigated results will be described and play a keen role in the study of nonlinear physical phenomena in the area of physics and engineering. [ABSTRACT FROM AUTHOR]

In this paper, we construct two kinds of q -differential integrable hierarchies. The first one is the q -universal character of B-type (BUC) and lattice q -BUC hierarchies expressed by q -shift operators. It is also shown that the lattice q -BUC hierarchy reduces to the q -BUC hierarchy with certain conditions. The other one is the q -deformed generalized symplectic Schur functions and the q -deformed generalized Q-functions defined by q -derivative operators. By means of the q -deformed vertex operators, the q -deformed symplectic universal character (SUC) and BUC hierarchies have been presented. Moreover, it is proved that q -deformed generalized symplectic Schur functions and generalized Q-functions are solutions of the q -deformed SUC and BUC hierarchies, respectively. Meanwhile, by using multi-component tau functions, we establish the multi-component q -deformed SUC and BUC hierarchies. In addition, based upon the discrete tau functions, the multi-component modified q -deformed SUC and BUC hierarchies have been discussed. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate Lie symmetries including Killing, homothetic and conformal symmetries of Lemaitre–Tolman–Bondi (LTB) spacetime metric. To find all LTB metrics admitting these three types of symmetries, we have analyzed the set of symmetry equations by a Maple algorithm that provides some restrictions on the functions involved in LTB metric under which this metric admits the three mentioned symmetries. The solution of symmetry equations under these restrictions leads to the explicit form of symmetries. The stress–energy tensor is calculated for all the obtained metrics in order to discuss their physical significance. It is noticed that most of these metrics satisfy certain energy conditions and correspond to anisotropic fluids. [ABSTRACT FROM AUTHOR]

In this paper, we present the coisotropic embedding theorem as a tool to provide a solution for the inverse problem of the calculus of variations for a particular class of implicit differential equations, namely the equations of motion of free Electrodynamics. [ABSTRACT FROM AUTHOR]

In this paper, we derive the Darboux solutions of Ito-type coupled KdV equation in Darboux framework which is associated with Hirota Satsuma systems. One of the main results is the generalization of Nth-fold Darboux solutions in terms of Wronskians. We also derive the exact multi-soliton solutions for the coupled field variables of that system in the background of zero seed solutions. With the addition of these findings, we also enrich our results with the graphical interpretations of interacting solitons which preserve their profiles after the collision as usually solitons possess such property intrinsically. Subsequently, we construct the equation of continuity that yields the infinite conserved quantities associated with interacting phenomenon of multi-solitons. [ABSTRACT FROM AUTHOR]