2017年, 第68卷, 第06期　
刊出日期：2017-12-01

  

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  A New Negative Discrete Hierarchy and Its N-Fold Darboux Transformation

  张宁, 夏铁成

  理论物理通讯. 2017, 68(06): 687-692.

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  Starting from a matrix discrete spectral problem, we derive a negative discrete hierarchy. It is shown that the hierarchy is integrable in the Liouville sense and possesses a bi-Hamiltonian structure. Furthermore, its N-fold Darboux transformation is established with the help of gauge transformation of Lax pair. As an application of the Darboux transformation, some new exact solutions for a discrete equation in the negative hierarchy are obtained.
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  Rogue Waves and Lump Solitons of the (3+1)-Dimensional Generalized B-type Kadomtsev-Petviashvili Equation for Water Waves

  孙岩, 田播, 刘磊, 柴汉鹏, 袁玉强

  理论物理通讯. 2017, 68(06): 693-700.

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  In this paper, the (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation for water waves is investigated. Through the Hirota method and Kadomtsev-Petviashvili hierarchy reduction, we obtain the first-order, higher-order, multiple rogue waves and lump solitons based on the solutions in terms of the Gramian. The first-order rogue waves are the line rogue waves which arise from the constant background and then disappear into the constant background again, while the first-order lump solitons propagate stably. Interactions among several first-order rogue waves which are described by the multiple rogue waves are presented. Elastic interactions of several first-order lump solitons are also presented. We find that the higher-order rogue waves and lump solitons can be treated as the superpositions of several first-order ones, while the interaction between the second-order lump solitons is inelastic.
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  Split Octonion Reformulation for Electromagnetic Chiral Media of Massive Dyons

  B. C. Chanyal

  理论物理通讯. 2017, 68(06): 701-710.

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  In an explicit, unified, and covariant formulation of an octonion algebra, we study and generalize the electromagnetic chiral fields equations of massive dyons with the split octonionic representation. Starting with 2×2 Zorn's vector matrix realization of split-octonion and its dual Euclidean spaces, we represent the unified structure of split octonionic electric and magnetic induction vectors for chiral media. As such, in present paper, we describe the chiral parameter and pairing constants in terms of split octonionic matrix representation of Drude-Born-Fedorov constitutive relations. We have expressed a split octonionic electromagnetic field vector for chiral media, which exhibits the unified field structure of electric and magnetic chiral fields of dyons. The beauty of split octonionic representation of Zorn vector matrix realization is that, the every scalar and vector components have its own meaning in the generalized chiral electromagnetism of dyons. Correspondingly, we obtained the alternative form of generalized Proca-Maxwell's equations of massive dyons in chiral media. Furthermore, the continuity equations, Poynting theorem and wave propagation for generalized electromagnetic fields of chiral media of massive dyons are established by split octonionic form of Zorn vector matrix algebra.
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  Reconstructing the Potential Function in a Formulation of Quantum Mechanics Based on Orthogonal Polynomials

  A. D. Alhaidari

  理论物理通讯. 2017, 68(06): 711-728.

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  In a recent reformulation of quantum mechanics, the properties of the physical system are derived from orthogonal polynomials that make up the expansion coefficients of the wavefunction in a complete set of square integrable basis. Here, we show how to reconstruct the potential function so that a correspondence with the standard formulation could be established. However, the correspondence places restriction on the kinematics of such problems.
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  Comparative Study of Entanglement and Wigner Function for Multi-Qubit GHZ-Squeezed State

  Fatima-Zahra Siyouri

  理论物理通讯. 2017, 68(06): 729-734.

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  In this paper we address the possibility of using the Wigner function to capture the quantum entanglement present in a multi-qubit system. For that purpose, we calculate both the degree of entanglement and the Wigner function for mixed tripartite squeezed states of Greenberger-Horne-Zeilinger (GHZ) type then we compare their behaviors. We show that the role of Wigner function in detecting and quantifying bipartite quantum correlation[Int. J. Mod. Phys. B 30 (2016) 1650187] may be generalized to the multipartite case.
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  A Type D Non-Vacuum Spacetime with Causality Violating Curves, and Its Physical Interpretation

  Faizuddin Ahmed

  理论物理通讯. 2017, 68(06): 735-740.

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  We present a topologically trivial, non-vacuum solution of the Einstein's field equations in four dimensions, which is regular everywhere. The metric admits circular closed timelike curves, which appear beyond the null curve, and these timelike curves are linearly stable under linear perturbations. Additionally, the spacetime admits null geodesics curve, which are not closed, and the metric is of type D in the Petrov classification scheme. The stress-energy tensor anisotropic fluid satisfy the different energy conditions and a generalization of Equation-of-State parameter of perfect fluid p=ωρ. The metric admits a twisting, shearfree, nonexapnding timelike geodesic congruence. Finally, the physical interpretation of this solution, based on the study of the equation of the geodesics deviation, will be presented.
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  Sliding Mode Control of Fractional-Order Delayed Memristive Chaotic System with Uncertainty and Disturbance

  丁大为, 刘芳芳, 陈辉, 王年, 梁栋

  理论物理通讯. 2017, 68(06): 741-748.

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  In this paper, a simplest fractional-order delayed memristive chaotic system is proposed in order to control the chaos behaviors via sliding mode control strategy. Firstly, we design a sliding mode control strategy for the fractional-order system with time delay to make the states of the system asymptotically stable. Then, we obtain theoretical analysis results of the control method using Lyapunov stability theorem which guarantees the asymptotic stability of the non-commensurate order and commensurate order system with and without uncertainty and an external disturbance. Finally, numerical simulations are given to verify that the proposed sliding mode control method can eliminate chaos and stabilize the fractional-order delayed memristive system in a finite time.
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  Anti-synchronization Between Two Coupled Networks with Unknown Parameters Using Adaptive and Pinning Controls

  孙田田, 李时兴, 孙伟刚

  理论物理通讯. 2017, 68(06): 749-754.

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  In this paper, we study anti-synchronization between two coupled networks where the node dynamics has an unknown system parameter. By designing adaptive and pinning control schemes, we realize the anti-synchronization. By Lyapunov stability theory, we obtain two theorems on the appearance of anti-synchronization. In addition, we derive a criterion for the pinning number of nodes. Finally we provide two numerical examples to show the effectiveness of our proposed control schemes. When the anti-synchronization is achieved, we successfully identify the unknown system parameter.
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  Infinite Conservation Laws, Continuous Symmetries and Invariant Solutions of Some Discrete Integrable Equations

  张玉峰, 张祥芝, 董焕河

  理论物理通讯. 2017, 68(06): 755-760.

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  Two new shift operators are introduced for which a few differential-difference equations are generated by applying the R-matrix method. These equations can be reduced to the standard Toda lattice equation and (1+1)-dimensional and (2+1)-dimensional Toda-type equations which have important applications in hydrodynamics, plasma physics, and so on. Based on these consequences, we deduce the Hamiltonian structures of two discrete systems. Finally, we obtain some new infinite conservation laws of two discrete equations and employ Lie-point transformation group to obtain some continuous symmetries and part of invariant solutions for the (1+1) and (2+1)-dimensional Toda-type equations.
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  New Exact Traveling Wave Solutions of the Unstable Nonlinear Schrödinger Equations

  K. Hosseini, D. Kumar, M. Kaplan, E. Yazdani Bejarbaneh

  理论物理通讯. 2017, 68(06): 761-767.

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  The present paper studies the unstable nonlinear Schrödinger equations, describing the time evolution of disturbances in marginally stable or unstable media. More precisely, the unstable nonlinear Schrödinger equation and its modified form are analytically solved using two efficient distinct techniques, known as the modified Kudraysov method and the sine-Gordon expansion approach. As a result, a wide range of new exact traveling wave solutions for the unstable nonlinear Schrödinger equation and its modified form are formally obtained.
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  General Solutions for Hydromagnetic Free Convection Flow over an Infinite Plate with Newtonian Heating, Mass Diffusion and Chemical Reaction

  Constatin Fetecau, Nehad Ali Shah, Dumitru Vieru

  理论物理通讯. 2017, 68(06): 768-782.

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  The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined. Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration, three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution (the steady-state), for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.
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  Damped Kadomtsev-Petviashvili Equation for Weakly Dissipative Solitons in Dense Relativistic Degenerate Plasmas

  S. Ahmad, Ata-ur-Rahman, S. A. Khan, F. Hadi

  理论物理通讯. 2017, 68(06): 783-790.

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  We have investigated the properties of three-dimensional electrostatic ion solitary structures in highly dense collisional plasma composed of ultra-relativistically degenerate electrons and non-relativistic degenerate ions. In the limit of low ion-neutral collision rate, we have derived a damped Kadomtsev-Petviashvili (KP) equation using perturbation analysis. Supplemented by vanishing boundary conditions, the time varying solution of damped KP equation leads to a weakly dissipative compressive soliton. The real frequency behavior and linear damping of solitary pulse due to ion-neutral collisions is discussed. In the presence of weak transverse perturbations, soliton evolution with damping parameter and plasma density is delineated pointing out the extent of propagation using typical parameters of dense plasma in the interior of white dwarfs.
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  Linear Analysis of Obliquely Propagating Longitudinal Waves in Partially Spin Polarized Degenerate Magnetized Plasma

  Z. Iqbal, G. Murtaza, A. Hussain

  理论物理通讯. 2017, 68(06): 791-797.

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  Linear analysis of low frequency obliquely propagating electrostatic waves in a partially spin polarized degenerate magnetized plasma is presented. Using Fourier analysis, a general linear dispersion relation is derived for low frequency electrostatic lower hybrid (LH) wave, ion acoustic (IA) wave and ion cyclotron (IC) wave in the presence of electron spin polarization. It is found that the electron spin polarization gives birth to a new spin-dependent wave (spin electron acoustic wave) in the spectrum of these waves. Further, the electron spin polarization also causes drastic shifts in the frequency spectrum of these waves. These effects would have a strong bearing on wave phenomena in degenerate astrophysical plasmas.
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  Influence of Cell-Cell Interactions on the Population Growth Rate in a Tumor

  陈勇

  理论物理通讯. 2017, 68(06): 798-802.

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  The understanding of the macroscopic phenomenological models of the population growth at a microscopic level is important to predict the population behaviors emerged from the interactions between the individuals. In this work, we consider the influence of the population growth rate R on the cell-cell interaction in a tumor system and show that, in most cases especially small proliferative probabilities, the regulative role of the interaction will be strengthened with the decline of the intrinsic proliferative probabilities. For the high replication rates of an individual and the cooperative interactions, the proliferative probability almost has no effect. We compute the dependences of R on the interactions between the cells under the approximation of the nearest neighbor in the rim of an avascular tumor. Our results are helpful to qualitatively understand the influence of the interactions between the individuals on the growth rate in population systems.
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  Rumor Spreading Model with Immunization Strategy and Delay Time on Homogeneous Networks

  王静, 王亚奇, 李敏

  理论物理通讯. 2017, 68(06): 803-810.

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  In order to prevent and control the spread of rumors, the implementation of immunization strategies for ignorant individuals is very necessary, where the immunization usually means letting them learn the truth of rumors. Considering the facts that there is always a delay time between rumor spreading and implementing immunization, and that the truth of rumors can also be spread out, this paper constructs a novel susceptible-infected-removed (SIR) model. The propagation dynamical behaviors of the SIR model on homogeneous networks are investigated by using the mean-field theory and the Monte Carlo method. Research shows that the greater the delay time, the worse the immune effect of the immunization strategy. It is also found that the spread of the truth can inhibit to some extent the propagation of rumors, and the trend will become more obvious with the increase of reliability of the truth. Moreover, under the influence of delay time, the existence of nodes' identification force still slightly reduces the propagation degree of rumors.