A special integrable nonlocal nonlinear Schrödinger equation, NNLS, or namely Alice-Bob NLS (ABNLS) equation is investigated. By means of the general N-th Darboux transformation, one can get various interesting solutions to display different types of structures especially for solitons. By using the Darboux transformation, its soliton solutions are obtained. Finally, by adjusting the values of free parameters, different kinds of solutions such as kinks, complexitons and rogue-wave solutions are explicitly exhibited. It is found that these solutions are quite different from the ones of the classical NLS equation.

In this paper, the Lie group classification method is performed on the fractional partial differential equation (FPDE), all of the point symmetries of the FPDEs are obtained. Then, the symmetry reductions and exact solutions to the fractional equations are presented, the compatibility of the symmetry analysis for the fractional and integer-order cases is verified. Especially, we reduce the FPDEs to the fractional ordinary differential equations (FODEs) in terms of the Erdélyi-Kober (E-K) fractional operator method, and extend the power series method for investigating exact solutions to the FPDEs.

A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated Legendre Equations are examined and established. The hypergeometric solutions, presented in this work, will promote future investigations of their mathematical properties and applications to problems in theoretical physics.

Here thermal dependence conductivity and nonlinear convection features in third-grade liquid flow bounded by moving surface having varying thickness are formulated. Stagnation point flow is considered. Revised FourierFick relations and double stratification phenomena are utilized for modeling energy and concentration expressions. Mathematical model of considered physical problem is achieved by implementing the idea of boundary layer theory. The acquired partial differential system is transformed into ordinary ones by employing relevant variables. The homotopic scheme yield convergent solutions of governing nonlinear expressions. Graphs are constructed for distinct values of physical constraints to elaborate the heat/mass transportation mechanisms.

Nonlocal symmetry and explicit solution of the integrable Alice-Bob modified Korteweg-de Vries (ABmKdV) equation is discussed, which has been established by the aid of the shifted parity and delayed time reversal to describe two-place events. Based on the Lax pair which contains the two-order partial derivative, the Lie symmetry group method is successfully applied to find the exact invariant solution for the AB-mKdV equation with nonlocal symmetry by introducing one suitable auxiliary variable. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to some specific functions are derived. Figures show the physical phenomenon, that is, "the shifted parity and delayed time reversal to describe two-place events".

The local approach to construct master equation for a composite open system with a weak internal coupling is simple and seems reasonable. However, it is thermodynamic consistent only when the subsystems are resonantly coupled. Efforts are being made to understand the inconsistency and test the validity of the local master equation. We present a perturbative method to solve the steady-state solutions of linear local master equations, which are demonstrated by two simple models. The solving process shows the stationary state as the result of competition between incoherent operations and the unitary creating quantum coherence, and consequently relate quantum coherence with thermodynamic consistency.

In this paper, a multi-proxy blind signature scheme based on controlled quantum teleportation is proposed. Entangled four-qubit Cluster state functions as quantum channel, which needs less resource to complete the quantum multi-proxy blind signature. The scheme uses the physical characteristics of quantum mechanics to guarantee its blindness, unforgeability, and undeniability. The eavesdropping check is used to ensure the security. Our scheme has a foreseeable application to the E-business, E-governments, and etc.

This article investigates the effects of variable thermal conductivity and variable mass diffusion coefficient on the transport of heat and mass in the flow of Casson fluid. Numerical simulations for two-dimensional flow induced by stretching surface are performed by using Galerkin finite element method (GFEM) with linear shape functions. After assembly process, nonlinear algebraic equations are linearized through Picard method and resulting linear system is solved iteratively using Gauss Seidal method with simulation tolerance 10^-8. Maximum value of independent variable η is searched through numerical experiments. Grid independent study was carried out and error analysis is performed. Simulated results are validated by comparing with already published results. Parametric study is carried out to explore the physics of the flow. The concentration increases when mass diffusion coefficient is increased. The concentration and thermal boundary layer thicknesses increase when ε₁ and ε are increased. The effect of generative chemical reaction on concentration is opposite to the effect of destructive chemical reaction on the concentration.

We investigate the decay of a₁⁺ (1260)→π⁺π⁺π^- with the assumption that the a₁(1260) is dynamically generated from the coupled channel ρπ and KK^* interactions. In addition to the tree level diagrams that proceed via a₁⁺ (1260)→ρ⁰π⁺→π⁺π⁺π^-, we take into account also the final state interactions of ππ→ππ and KK→ππ. We calculate the invariant π⁺π^- mass distribution and also the total decay width of a₁⁺ (1260)→π⁺π⁺π^- as a function of the mass of a₁(1260). The calculated total decay width of a₁(1260) is significantly different from other model calculations and tied to the dynamical nature of the a₁(1260) resonance. The future experimental observations could test of model calculations and would provide vary valuable information on the relevance of the ρπ component in the a₁(1260) wave function.

One of the cluster behaviors observed in light nuclei such as ²⁰Ne and ⁴⁴Ti is the presence of an alpha particle rotating around a double magic number core. In this work, a theoretical method is used for investigation of rotational spectra of two-particle cluster states. To this end, Deng-Fan potential in addition to Hellman potential is used as the core and cluster potential. Next, given the Wildermuth condition, and proper quantum numbers describing the relative motion of the alpha particle and core, the rotational levels of ²⁰Ne and ⁴⁴Ti isotopes are calculated. Our studies show that the results are in good agreement with the available data.

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption. Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method (HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.

The effects of electron correlations and spin-orbit coupling on the magnetic anisotropy in the antiferromagnetically ordered 5d perovskite iridates Sr₂IrO₄ is investigated theoretically using a microscopic model includes a realistic five-orbital tight-binding Hamiltonian, atomic spin-orbit coupling, and multi-orbital Hubbard interactions. Hartree-Fock approximation is applied to obtain the ground state properties with varying spin-orbit coupling and electron correlations. We demonstrate that the interplay between the atomic intraorbital Coulomb repulsion and the Hund's rule coupling leads to a remarkable variability of the resulting magnetic anisotropy at a constant nonzero spin-orbit coupling. At the same time, the preferred direction of the ordered antiferromagnetical moment remains unaltered upon changes in the strength of spin-orbit coupling.

In this investigation we analyze the rotating three-dimensional magnetohydrodynamic flow of Maxwell fluid in attendance of binary chemical reaction with activation energy. Furthermore, effects of non-Fourier heat flux are taken into account. Formulation is done in the presence of heat and mass convective boundary conditions. Self-similar forms from boundary layer equations are obtained using apposite transformations. Numerical solution is obtained via built-in bvp-4c function in MATLAB for the system of differential equations. Effects of ensuing parameters on flow distributions are portrayed graphically. It is witnessed that increasing values of rotational parameter lowers the velocity profile and both Biot numbers have escalating effect on temperature and concentration distributions. A comparative study to a previously done investigation is also included to corroborate our results.

Optically levitated nano-particle with spins is a promising system for high-precision measurement and quantum information processing. We theoretically analyze the ratio between the fluctuation of particle's displacement caused by spins in magnetic field and caused by molecular collisions of the residual air. When the ratio is larger than unity, the displacement fluctuation of spins flipping can be remarkably detected. By theoretical analysis and numerical simulation, we propose and validate a scheme for the detection of gradient of the magnetic field by levitating ferromagnetic nano-particle, and also put forward a realizable detection scheme of the single spin by levitating nano-diamond particle with single nitrogen-vacancy(NV) centers.

The present work aims to investigate transverse Oldroyd-B nanofluid flow on a stretched panel with consideration of internal heat generation. Buongiorno model is utilized to study influence of thermophoresis and Brownian motion effects. A numerical procedure known as Keller box algorithm is used to solve the governed physical model. Graphically velocity, temperature and concentration of nanoparticles are expressed. Also, concerned physical measures such as heat and mass transfer are investigated numerically. The simulations performed revealed that fluid parameters play a significant role in heat transfer under Brownian motion and thermophoresis effects. Local heat flux is elevated while local mass flux is suppressed with enhancing Brownian motion parameter. Streamlines pattern exhibits that flow is more inclined in the presence of Deborah number effects. To the best of our knowledge, transverse flow of an Oldroyd-B type fluid which incorporates the thermal relaxation effects has never been reported before in the presence of Brownian motion and internal heating phenomenon. Therefore we intend to discuss these features in detail. The obtained results are a novel contribution, which can be benchmark for further relevant academic research related to polymer industry.

The Bäcklund transformation(BT) of the mKdV-sG equation is constructed by introducing a new transformation. Infinitely many nonlocal symmetries are obtained in terms of its BT. The soliton-periodic wave interaction solutions are explicitly derived by the classical Lie-group reduction method. Particularly, some special concrete soliton and periodic wave interaction solutions and their behaviours are discussed both in analytical and graphical ways.

The discriminating strength D_S(ρ_AB) induced by local Gaussian unitary operators for any (n+m)-mode Gaussian state ρ_AB is introduced in[Phys. Rev. A 83 (2011) 042325]. In this paper, we further discuss the quantity by restricting to Hilbert-Schmidt norm. The analytic formulas of DS for two-mode squeezed thermal states and mixed thermal states are given. Then, the relationship between D_S(ρ_AB) and D_S((I ⊗ Φ)(ρ_AB)) for some special Gaussian channels Φ is discussed. In addition, D_S is compared with Gaussian entanglement for symmetric squeezed thermal states.

We investigate solitary vortex evolution in two-dimensional Bose-Einstein condensates based on the Gross-Pitaevskii equation model. Through the variational method, together with the novel Gaussian ansatz incorporating asymmetric perturbation effects, we arrive at the analytical solitary vortex solution with two typical forms:a symmetric quasi-stable solution under certain parametric settings and a diverging propagation case arising from an initial asymmetric perturbation. The derived pictorial evolutionary patterns of the solitary vortices are compared with those from a pure numerical analysis, and by identifying the key qualitative features, we show the applicability of the theoretical treatment presented here.

In this paper, we study coherence-induced state ordering with Tsallis relative entropy of coherence, relative entropy of coherence and l₁ norm of coherence, and give the sufficient conditions of the same state order induced by above coherence measures. First, we show that the above measures give the same ordering for single-qubit states in some special cases. Second, we consider some special states in a d-dimensional quantum system. We show that the above measures generate the same ordering for these special states. Finally, we discuss dynamics of coherence-induced state ordering under Markovian channels. We find amplitude damping channel changes the coherence-induced ordering even though for single-qubit states with fixed mixedness.

In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution, which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance.

We study some novel patterns of rogue wave in the coupled cubic-quintic nonlinear Schrödinger equations. Utilizing the generalized Darboux transformation, the higher-order rogue wave pairs of the coupled system are generated. Especially, the first-and second-order rogue wave pairs are discussed in detail. It demonstrates that two classical fundamental rogue waves can be emerged from the first-order case and four or six classical fundamental rogue waves from the second-order case. In the second-order rogue wave solution, the distribution structures can be in triangle, quadrilateral and ring shapes by fixing appropriate values of the free parameters. In contrast to single-component systems, there are always more abundant rogue wave structures in multi-component ones. It is shown that the two higher-order nonlinear coefficients ρ₁ and ρ₂ make some skews of the rogue waves.

In the new framework of gravitational quantum field theory (GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93 (2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.

In response to the present status that searching for SUSY particles has been unsuccessful, we propose a bold scenario that SUSY particles are confined inside hadrons with a required condition of P_R=1 in analog to the color confinement for quarks. The scenario seems to be able to reconcile the beautiful SUSY theory and non-observation at present experiments. On other aspects, some loopholes in the proposal emerge and require to be answered in the future research.

The non-relativistic radial Schrödinger equation is analytically solved using asymptotic iteration method within the framework of a general interaction potential whose special cases are the Cornell and Cornell plus harmonic potentials. The energy eigenvalues expression is derived in three dimensional space, which is further used to calculate the mass spectra of cc, bb, bc, cs, bs and bq mesons. The obtained results of this work are in good agreement with experimental and other relativistic results and also improved in comparison with other non-relativistic recent studies.

In a paper[Gen. Relativ. Gravit. 48 (2016) 57] Chakrabarti and Banerjee investigated perfect fluid collapse in f(R) gravity model and claimed that such a collapse is possible. In this paper we show that without the assumption of dark energy it is not possible that perfect fluid spherical gravitational collapse will occur. We have solved the field equations by assuming linear equation of state (p=ωμ) in metric f(R) gravity with ω=-1. It is shown that Chakrabarti and Banerjee reached to false conclusion as they derived wrong field equations. We have also discussed formation of apparent horizon and singularity.

The main purpose of this paper is to investigate energy bounds in the context of f(R,G) gravity. To meet this aim, we choose static spherically symmetric spacetime in f(R,G) gravity to develop the field equations. We select three different models of f(R,G) gravity, which are thoroughly discussed in the literature. Firstly, the inequalities are formulated using energy bounds and then viability of the considered models are checked respectively. Graphical analysis show that specific f(R,G) gravity models are satisfied under suitable values of model parameters. It is shown that in a certain case energy bounds are satisfied expect SEC, which supports the late time acceleration expansion of unverse.

Similarity solution for a spherical shock wave with or without gravitational field in a dusty gas is studied under the action of monochromatic radiation. It is supposed that dusty gas be a mixture of perfect gas and micro solid particles. Equilibrium flow condition is supposed to be maintained and energy is varying which is continuously supplied by inner expanding surface. It is found that similarity solution exists under the constant initial density. The comparison between the solutions obtained in gravitating and non-gravitating medium is done. It is found that the shock strength increases with an increase in gravitational parameter or ratio of the density of solid particles to the initial density of the gas, whereas an increase in the radiation parameter has decaying effect on the shock waves.

The role of viscosity coefficient (η'), coulomb coupling parameter (Γ) and dust mass on the growth of jeans mode is investigated in strongly coupled dusty plasma using equations of Generalized Hydrodynamics (GH) Model. The novel aspect of this work is that the force arising due to electrostatic pressure caused by grain grain interaction has been included in the dynamics of dust particles. This force is found to play a significant role in counter balancing the self gravity effect, thereby reducing the growth rate of jeans instability. The present work may provide more physical insight in understanding the mechanisms behind formation of planetesimals, stars etc.

We theoretically propose a photonic flash based on a linearly coupled cavity system. Via driving the two side cavities by external fields, it forms a cyclic energy-level diagram and therefore the phase difference between the driving fields acts as a controller of the steady state due to the quantum interference effect. In the optical trimer structure, we show that the perfect photonic flash can be realized in the situation of resonant driving. The perfect photonic flash scheme is furthermore generalized to multiple coupled cavity system, where the cavities with odd and even number turn bright and dark alternatively. Our proposal may be applied for designing the quantum neon and realizing a controllable photonic localization.

Effect of critical beam radius on self-focusing of cosh-Gaussian laser beams in collisionless magnetized plasma under ponderomotive nonlinearity forms the main core of present work. To investigate propagation dynamics of cosh-Gaussian laser beams in collisionless magnetized plasma, well established parabolic equation approach under WKB and paraxial approximations is employed. Our study is crucially pivoted on the concept of critical curve and subsequent determination of numerical interval for decentered parameter to sustain the competition between diffraction and self-focusing during the propagation of laser beam. Additionally, in the present study an interesting feature in the self-focusing region of the critical curve has been attempted for different values of decentered parameter.

In this paper, we use a nonlinear decohering quantum model to study the initial step of photosynthesis which is an ultrafast transfer process of absorption the sunlight by light-harvesting complexes and electronic excitation transfer to the reaction center (RC). In this decohering model, the Hamiltonian of the system commutes with the systemenvironment interaction. We take B850 ring of light-harvesting complex Ⅱ (LH-Ⅱ) in purple bacteria as an example to calculate the efficiency of the energy transfer as a function of time. We find that the environmental noise can make the LH-Ⅱ have stable energy transfer efficiency over a long time. This is to say that the environmental noise which is the decohering source has advantage of the energy transfer in the process of photosynthesis.

This paper investigates the three-dimensional flow of a Sisko fluid over a bidirectional stretching sheet, in a porous medium. By using the effect of Cattaneo-Christov heat flux model, heat transfer analysis is illustrated. Using similarity transformation the governing partial differential equations are transferred into a system of ordinary differential equations that are solved numerically by applying Nachtsheim-Swigert shooting iteration technique along with the 6-th order Runge-Kutta integration scheme. The effect of various physical parameters such as Sisko fluid, ratio parameter, thermal conductivity, porous medium, radiation parameter, Brownian motion, thermophoresis, Prandtl number, and Lewis number are graphically represented.

Presence of external electrical field plays a vital role in heat transfer and fluid flow phenomena. Keeping this in view present article is a numerical investigation of stagnation point flow of water based nanoparticles suspended fluid under the influence of induced magnetic field. A detailed comparative analysis has been performed by considering Copper and Titanium dioxide nanoparticles. Utilization of similarity analysis leads to a simplified system of coupled nonlinear differential equations, which has been tackled numerically by means of shooting technique followed by Runge-Kutta of order 5. The solutions are computed correct up to 6 decimal places. Influence of pertinent parameters is examined for fluid flow, induced magnetic field, and temperature profile. One of the key findings includes that magnetic parameter plays a vital role in directing fluid flow and lowering temperature profile. Moreover, it is concluded that Cu-water based nanofluid high thermal conductivity contributes in enhancing heat transfer efficiently.

A generalized nonautonomous nonlinear equation, which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber, is investigated. N-soliton solutions for such an equation are constructed and verified with the Wronskian technique. Collisions among the three solitons are discussed and illustrated, and effects of the coefficients σ₁(x, t), σ₂(x, t), σ₃(x, t) and v(x, t) on the collisions are graphically analyzed, where σ₁(x, t), σ₂(x, t), σ₃(x, t) and v(x, t) are the first-, second-, third-order dispersion parameters and an inhomogeneous parameter related to the phase modulation and gain(loss), respectively. The head-on collisions among the three solitons are observed, where the collisions are elastc. When σ₁(x, t) is chosen as the function of x, amplitudes of the solitons do not alter, but the speed of one of the solitons changes. σ₂(x, t) is found to affect the amplitudes and speeds of the two of the solitons. It reveals that the collision features of the solitons alter with σ₃(x, t)=-1.8x. Additionally, traveling directions of the three solitons are observed to be parallel when we change the value of v(x, t).

In this paper, an extended multi-dimensional N-coupled higher-order nonlinear Schrödinger equation (NCHNLSE), which can describe the propagation of the ultrashort pulses in wavelength division multiplexing (WDM) systems, is investigated. By the bilinear method, we construct the breather solutions for the extended (1+1), (2+1) and (3+1)-dimensional N-CHNLSE. The rogue waves are derived as a limiting form of breathers with the aid of symbolic computation. The effect of group velocity dispersion (GVD), third-order dispersion (TOD) and nonlinearity on breathers and rogue waves solutions are discussed in the optical communication systems.

The Hermitian surface momentum operator for a particle confined to a 2D curved surface spanned by orthogonal coordinates and embedded in 3D space is expressed as a symmetric expression in derivatives with respect to the surface coordinates and so is manifestly along the surface. This is an alternative form to the one reported in the literature and usually named geometric momentum, which has a term proportional to the mean curvature along the direction normal to the surface, and so "apparently" not along the surface. The symmetric form of the momentum is the sum of two symmetric Hermitian operators along the two orthogonal directions defined by the surface coordinates. The centripetal force operator for a particle on the surface of a cylinder and a sphere is calculated by taking the time derivative of the momentum and is seen to be a symmetrization of the well-known classical expressions.

The dissipative dynamics of non-coupled two qubits interacting with independent reservoir is studied by solving the non-Markovian master equation. In order to examine the effectiveness of the Nakajima-Zwanzig and timeconvolutionless master equations in the description of quantum correlation dynamics, different coupled regimes are investigated. The comparison between the above two master equation methods for investigating the dynamics of quantum discord is also made. Finally, we further confirm that the two master equations should be applied in different regimes of qubits coupled to their reservoirs, respectively.

We develop a master equation approach to describe the dynamics of distant resonators coupled through a one-dimensional waveguide. Our method takes into account the back-actions of the reservoirs, and enables us to calculate the exact dynamics of the complete system at all times. We show that such system can cause nonexponential and long-lived photon decay due to the existence of a relaxation effect. The physical origin of non-Markovianity in our model system is the finite propagation speed resulting in time delays in communication between the nodes, and strong decay rate of the emitters into the waveguide. When the distance satisfies the standing wave condition, we find that when the time delay is increased, the dark modes formation is no longer perfect, and the average photon number of dark mode decreases in steady time limit.

The aim of this paper is to study the Herglotz variational principle of the fractional Birkhoffian system and its Noether symmetry and conserved quantities. First, the fractional Pfaff-Herglotz action and the fractional PfaffHerglotz principle are presented. Second, based on different definitions of fractional derivatives, four kinds of fractional Birkhoff's equations in terms of the Herglotz variational principle are established. Further, the definition and criterion of Noether symmetry of the fractional Birkhoffian system in terms of the Herglotz variational problem are given. According to the relationship between the symmetry and the conserved quantities, the Noether's theorems within four different fractional derivatives are derived, which can reduce to the Noether's theorem of the Birkhoffian system in terms of the Herglotz variational principle under the classical conditions. As applications of the Noether's t heorems of the fractional Birkhoffian system in terms of the Herglotz variational principle, an example is given at the end of this paper.