Table of contents

A new (γ_A, σ_B)-matrix KP hierarchy with two time series γ_A and σ_B, which consists of γ_A-flow, σ_B-flow and mixed γ_A and σ_B-evolution equations of eigenfunctions, is proposed. The reduction and constrained flows of (γ_A, σ_B)-matrix KP hierarchy are studied. The dressing method is generalized to the (γ_A, σ_B)-matrix KP hierarchy and some solutions are presented.

We investigate analytical solutions of the (2+1)-dimensional combining cubic-quintic nonlinear Schrödinger (CQNLS) equation by the classical Lie group symmetry method. We not only obtain the Lie-point symmetries and some (1+1)-dimensional partial differential systems, but also derive bright solitons, dark solitons, kink or anti-kink solutions and the localized instanton solution.

In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the δ expansion method (created to deal with problems in Quantum Field Theory) which will enable both the linearization and perturbation expansion of such equations. Such a method allows for one to quickly obtain the order zero perturbation theory in terms of certain special functions which are governed by linear equations. Higher order perturbation theories can then be obtained in terms of such special functions. One benefit to such a method is that it may be applied even to models without small physical parameters, as the perturbation is given in terms of the degree of nonlinearity, rather than any physical parameter. As an application, we discuss a method of linearizing the six Painlevé equations by an application of the method. In addition to highlighting the benefits of the method, we discuss certain shortcomings of the method.

In this paper, we study the influence of the size of interaction neighbors (k) on the evolution of cooperation in the spatial snowdrift game. At first, we consider the effects of noise K and cost-to-benefit ratio r, the simulation results indicate that the evolution of cooperation depends on the combined action of noise and cost-to-benefit ratio. For a lower r, the cooperators are multitudinous and the cooperation frequency ultimately increases to 1 as the increase of noise. However, for a higher r, the defectors account for the majority of the game and dominate the game if the noise is large enough. Then we mainly investigate how k influences the evolution of cooperation by varying the noise in detail. We find that the frequency of cooperators is closely related to the size of neighborhood and cost-to-benefit ratio r. In the case of lower r, the augmentation of k plays no positive role in promoting the cooperation as compared with that of k = 4, while for higher r the cooperation is improved for a growing size of neighborhood. At last, based on the above discussions, we explore the cluster-forming mechanism among the cooperators. The current results are beneficial to further understand the evolution of cooperation in many natural, social and biological systems.

When a population structure is modelled as a square lattice, the cooperation may be improved for an evolutionary prisoner dilemma game or be inhibited for an evolutionary snowdrift game. In this work, we investigate cooperation in a population on a square lattice where the interaction among players contains both prisoner dilemma game and snowdrift game. The heterogeneity in interaction is introduced to the population in two different ways: the heterogenous character of interaction assigned to every player (HCP) or the heterogenous character of interaction assigned to every link between any two players (HCL). The resonant enhancement of cooperation in the case of HCP is observed while the resonant inhibition of cooperation in the case of HCL is prominent. The explanations on the enhancement or inhibition of cooperation are presented for these two cases.

The second Poincaré kinematical group serves as one of new ones in addition to the known possible kinematics. The geometries with the second Poincaré symmetry is presented and their properties are analyzed. On the geometries, the new mechanics based on the principle of relativity with two universal constants (c, l) can be established.

By employing Hirota bilinear method and Riemann theta functions of genus one, explicit triply periodic wave solutions for the (2+1)-dimensional Boussinesq equation are constructed under the Backlund transformation u = (1/6)(u₀ − 1) + 2[ln f(x, y, t)]_xx, four kinds of triply periodic wave solutions are derived, and their long wave limit are discussed. The properties of one of the solutions are shown in Fig. 1.

We have constructed explicit nonautonomous soliton solutions of the generalized nonlinear Schrödinger equation in the (3+1)-dimensional inhomogeneous cubic-quintic nonlinear medium. The gain parameter has no effects on the motion of the soliton's phase or their velocities, and it affects just the evolution of their peaks. As two examples, we discuss the propagation of nonautonomous solitons in the periodic distributed amplification system and the exponential dispersion decreasing system. Results show that the presence of the chirp not only makes the intensity of solitons weaken more promptly, but also broadens their width.

Recently, there are two independent approaches related to a class of nonlinear Lie algebras of three generators; and the realizations of these generators are achieved respectively in Schwinger-boson and position representation. However, by use of the representation transformation between these two representations, the equivalence of the two realizations is therefore proved.

A quantum steganography communication scheme via Greenberger-Horne-Zeilinger GHZ₄ state is constructed to investigate the possibility of remotely transferred hidden information. Moreover, the multipartite entangled states are become a hectic topic due to its important applications and deep effects on aspects of quantum information. Then, the scheme consists of sharing the correlation of four particle GHZ₄ states between the legitimate users. After insuring the security of the quantum channel, they begin to hide the secret information in the cover of message. Comparing the scheme with the previous quantum steganographies, capacity and imperceptibility of hidden message are good. The security of the present scheme against many attacks is also discussed.

In this paper, a quantum private comparison protocol is proposed based on bell entangled states. In our protocol, two parties can compare the equality of their information with the help of a semi-honest third party. The correctness and security of our protocol are discussed. One party cannot learn the other's private information and the third party also cannot learn any information about the private information.

For a pure non-markovian dephasing model we derive analytic expressions of coherent information, quantum discord, and entanglement. We find that for the cases of the initial Werner states, the dynamical behavior of coherent information is similar to that of quantum discord but different from that of entanglement. Coherent information, as well as quantum discord, can reveal the quantum correlations in some mixed-states, in which the entanglement is zero.

The higher-order interactions of Bose-Einstein condensate in multi-dimensional optical lattices are discussed both analytically and numerically. It is demonstrated that the effects of the higher-order atomic interactions on the sound speed and the stabilities of Bloch waves strongly depend on the lattice strength. In the presence of higher-order effects, tighter and high-dimensional lattices are confirmed to be two positive factors for maintaining the system's energetic stability, and the dynamical instability of Bloch waves can take place simultaneously with the energetic instability. In addition, we find that the higher-order interactions exhibit a long-range behavior and the long-lived coherent Bloch oscillations in a tilted optical lattice exist. Our results provide an effective way to probe the higher-order interactions in optical lattices.

In this paper, we discuss the coefficients of Gravitational waveform due to eccentric binaries periastron advance with evolved eccentricity. For the basic harmonic modes (n ≤ 5), the frequency split and corresponding relative strengths in the spectrum are figured out. Taking the well known binary systems PSRB 1913+16 and PSRB 1534+12 as examples, we study the dominant harmonic and its frequency split caused by periastron advance in the spectra, and give an estimation of detectability for PSRB 1913+16 and PSRB 1534+12, which are the promising targets for space observatories of gravitational wave.

It is known that Gauss-Bonnet terms in higher dimensional gravity can produce an effective cosmological constant. We add extra examples to this picture by presenting explicitly two branches of accelerating vacuum solutions to the Einstein-Gauss-Bonnet gravities with a bare cosmological constant in 5 and 6 dimensions. Both branches of solutions are of constant curvature and the effective cosmological constants are independent of the acceleration parameter. One branch (the "−" branch) of the solutions is well defined in the limit when the Gauss-Bonnet parameter approaches zero, in which case the effective cosmological constant becomes identical with the bare value, while the other (i.e. the "+") branch is singular in the same limit, and beyond this singular limit, the effective cosmological constant is inversely proportional to the Gauss-Bonnet parameter with a negative constant of proportionality when the bare value vanishes.

The surface density Σ-map and the convergence κ-map of Bullet Cluster 1E0657-558 show that the center of baryonic matters separates from the center of gravitational force, and the distribution of gravitational force do not possess spherical symmetry. This hints that a modified gravity with difference to Newtonian inverse-square law at large scale, and less symmetry is worth investigating. In this paper, we study the dynamics in Randers-Finsler spacetime. The Newtonian limit and gravitational deflection of light in a Rindler-type potential is focused in particular. It is shown that the convergence in Finsler spacetime could account for the observations of Bullet Cluster.

One-species competition ecosystem with noise and time delay was investigated as not driven by a periodic force. The results show that the time delay is responsible for stochastic resonance of the system as delay time is smaller than critical point of the Hopf bifurcation.

This paper investigates second-order consensus of multi-agent systems with a virtual leader of varying velocity while preserving network connectivity. We propose a novel second-order consensus algorithm with bounded control inputs. Under the condition that the initial network is connected, the network will be connected all the time and all agents and the virtual leader can attain the same position and move with the same velocity. A simulation example is proposed to illustrate the effective of the proposed algorithm.

We revisit quantum gravitational contributions to quantum gauge field theories in the gauge condition independent Vilkovisky—DeWitt formalism based on the background field method. With the advantage of Landau-DeWitt gauge, we explicitly obtain the gauge condition independent result for the quadratically divergent gravitational corrections to gauge couplings. By employing, in a general way, a scheme-independent regularization method that can preserve both gauge invariance and original divergent behavior of integrals, we show that the resulting gauge coupling is power-law running and asymptotically free. The regularization scheme dependence is clarified by comparing with results obtained by other methods. The loop regularization scheme is found to be applicable for a consistent calculation.

In this paper we will analyse the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory in superspace formalism. We then study the quantum gauge transformations for this ABJM theory in gaugeon formalism. We will also analyse the extended BRST symmetry for this ABJM theory in gaugeon formalism and show that these BRST transformations for this theory are nilpotent and this in turn leads to the unitary evolution of the S-matrix.

Light-front holography leads to a rigorous connection between hadronic amplitudes in a higher dimensional anti-de Sitter (AdS) space and frame-independent light-front wavefunctions of hadrons in (3 + 1)-dimensional physical space-time, thus providing a compelling physical interpretation of the AdS/CFT correspondence principle and AdS/QCD, a useful framework which describes the correspondence between theories in a modified AdS₅ background and confining field theories in physical space-time. To a first semiclassical approximation, where quantum loops and quark masses are not included, this approach leads to a single-variable light-front Schrödinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate ζ which measures the separation of the constituents within a hadron at equal light-front time. The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role. We give an overview of the light-front holographic approach to strongly coupled QCD. In particular, we study the photon-to-meson transition form factors (TFFs) F_Mγ(Q²) for γ* → M using light-front holographic methods. The results for the TFFs for the η and η' mesons are also presented. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates. A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.

In the framework of the NRQCD factorization formalism, we calculate the decay rate for the process ϒ(1S) → cgg to the next-to-leading order (NLO) in the relative velocity v of the b quark in the bottomonium rest frame. We also study the momentum distributions of the charm quark and the charmed-hadron in the decay. The momentum distribution of the charmed-hadron is obtained by convolving the charm quark momentum distribution with a fragmentation function of the charm quark into the hadron. In addition, we fit the nonperturbative NRQCD matrix element ⟨v²⟩_ϒ through comparing the theoretical prediction with the measurement from the BaBar collaboration for the decay rate of ϒ(1S) → D*⁺X. In return, taking this matrix element as an input parameter, we predict the decay rates as well as the momentum distributions for a collection of charmed-hadrons in the process ϒ(1S) → cgg → hX.

The effects from quantum coherence via decays and incoherent pumping on the lasing without inversion (LWI) are investigated in a four-level system. By analyzing the transient and steady-state behaviors of the absorption, we find that the gain occurs when both spontaneously generated coherence (SGC) and coherence induced by incoherent pumping (IPC) are considered. We attribute the occurrence of the gain to the interaction of quantum coherence via decays and incoherent pumping.

We present an improved lattice Boltzmann (LB) model for thermal liquid-vapor system. In the new model, the Windowed Fast Fourier Transform (WFFT) and its inverse are used to calculate both the convection term and the external force term of the LB equation. By adopting the WFFT scheme, Gibbs oscillations can be damped effectively in unsmooth regions while high resolution feature of the spectral method can be retained in smooth regions. As a result, spatial discretization errors are dramatically decreased, conservation of the total energy is much better preserved, and the spurious velocities near the liquid-vapor interface are significantly reduced. The high resolution, together with the low complexity of the WFFT approach, endows the proposed method with considerable potential for studying a wide class of problems in the field of multiphase flows.

Simple arguments are used to construct a model to explain the extreme ultraviolet radiation conversion efficiency (EUV-CE) of a tin-based droplet target laser produced plasmas by calculating the laser absorption efficiency, radiation efficiency, and spectral efficiency. The dependence of drive laser pulse duration and laser intensity on EUV-CE is investigated. The results show that at some appropriate laser intensity, where the sum energy of the thermal conduction, out-off band radiation and plasma plume kinetic losses is at a minimum, the EUV-CE should reach a maximum. The EUV-CE predicted by the present simple model is also compared with the available experimental and simulation data and a fair agreement between them is found.

In this paper, we study a long-range percolation model on the lattice ^d with multi-type vertices and directed edges. Each vertex x ∊ ^d is independently assigned a non-negative weight W_x and a type ψ_x, where (W_x)_x∊^d are i.i.d. random variables, and (ψ_x)_x∊^d are also i.i.d. Conditionally on weights and types, and given λ, α > 0, the edges are independent and the probability that there is a directed edge from x to y is given by p_xy = 1 − exp(−λφ_ψxψy W_xW_y/|x−y|^α), where φ_ij's are entries from a type matrix Φ. We show that, when the tail of the distribution of W_x is regularly varying with exponent τ − 1, the tails of the out/in-degree distributions are both regularly varying with exponent γ = α(τ − 1)/d. We formulate conditions under which there exist critical values λ_c^WCC ∊ (0, ∞) and λ_c^SCC ∊ (0, ∞) such that an infinite weak component and an infinite strong component emerge, respectively, when λ exceeds them. A phase transition is established for the shortest path lengths of directed and undirected edges in the infinite component at the point γ = 2, where the out/in-degrees switch from having finite to infinite variances. The random graph model studied here features some structures of multi-type vertices and directed edges which appear naturally in many real-world networks, such as the SNS networks and computer communication networks.

Considering in symmetrical half-length bond operations, we present in this paper two types of newly-developed generalizations of the remarkable Migdal-Kadanoff bond-moving renormalization group transformation recursion procedures. The predominance in application of these generalized procedures are illustrated by making use of them to study the critical behavior of the spin-continuous Gaussian model constructed on the typical translational invariant lattices and fractals respectively. Results such as the correlation length critical exponents obtained by these means are found to be in good conformity with the classical results from other previous studies.

Using the first-principles band-structure method and a special quasirandom structure (SQS) approach, we have systematically calculated the alloy bowing coefficients and the nature band offsets of Sn_xZn_1−xTe alloys. We show that the bowing coefficients and band gaps of these alloys are sensitively composition dependent. Due to wave functions full overlapping and delocalization of the Sn outermost p orbits and Zn s orbits, the coupling between these states is very strong, resulting in a significant downshift of conduction band edge with the increase of the Sn concentration x, While the valence band edge keeps almost unchanged compared with that of the binary ZnTe, thus improving the possibility for ambipolar-doping.

The two dimensions hole-doped t—t'—J—U model was studied based on the Gutzwiller approach and the renormalized mean-field theory. The phase diagrams of gossamer superconductors and the effects of the next-nearest-neighbor hopping (t') on superconductivity and antiferromagnetism based on the t—t'—J—U model were investigated. The results show that the qualitative feature of the phase diagrams in the t—t'—J—U model is the same as in the case of the t—J—U model. The antiferromagnetic order coexists with the d-wave superconductivity (dSC) in the underdoped region below the doping δ ≈ 0.1 and is enhanced by the t'. The dSC order is slightly suppressed by t' in the underdoped region and greatly enhanced in the overdoped region. The dSC order is pushed to a larger doping region and the coexistence region of the AF and dSC extends to higher doping.