Table of contents

A complete approximate symmetry classification of a class of perturbed nonlinear wave equations is performed using the method originated from Fushchich and Shtelen. Moreover, large classes of approximate invariant solutions of the equations based on the Lie group method are constructed.

In the present paper, with the aid of symbolic computation, families of new nontrivial solutions of the first-order sub-ODE F'² = AF² + BF^2+p + CF^2+2p (where F' = dF/dξ, p > 0) are obtained. To our best knowledge, these nontrivial solutions have not been found in [X.Z. Li and M.L. Wang, Phys. Lett. A 361 (2007) 115] and [S. Zhang, W. Wang, and J.L. Tong, Phys. Lett. A 372 (2008) 3808] and other existent papers until now. Using these nontrivial solutions, the sub-ODE method is described to construct several kinds of exact travelling wave solutions for the generalized KdV-mKdV equation with higher-order nonlinear terms and the generalized ZK equation with higher-order nonlinear terms. By means of this method, many other physically important nonlinear partial differential equations with nonlinear terms of any order can be investigated and new nontrivial solutions can be explicitly obtained with the help of symbolic computation system Maple or Mathematica.

Based on the concept of adiabatic invariant, the perturbation to Mei symmetry and adiabatic invariants for nonholonomic mechanical systems in terms of quasi-coordinates are studied. The definition of the perturbation to Mei symmetry for the system is presented, and the criterion of the perturbation to Mei symmetry is given. Meanwhile, the Mei adiabatic invariants for the perturbed system are obtained.

In this paper, using the generalized (G'/G)-expansion method and the auxiliary differential equation method, we discuss the (2+1)-dimensional canonical generalized KP (CGKP), KdV, and (2+1)-dimensional Burgers equations with variable coefficients. Many exact solutions of the equations are obtained in terms of elliptic functions, hyperbolic functions, trigonometric functions, and rational functions.

Based on the Pfaffian derivative formulae, a Grammian determinant solution for a (3+1)-dimensional soliton equation is obtained. Moreover, the Pfaffianization procedure is applied for the equation to generate a new coupled system. At last, a Gram-type Pfaffian solution to the new coupled system is given.

In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the (2+1)-dimensional Kaup–Kupershmidt (KK) equation are presented. We successfully obtain more general exact travelling wave solutions for (2+1)-dimensional KK equation by the symmetry method and the (G'/G)-expansion method. Consequently, we find some new solutions of (2+1)-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions.

An improved algorithm for symbolic computation of Hirota bilinear forms of KdV-type equations with logarithmic transformations is presented. In the algorithm, the general assumption of Hirota bilinear form is successfully reduced based on the property of uniformity in rank. Furthermore, we discard the integral operation in the traditional algorithm. The software package HBFTrans is written in Maple and its running effectiveness is tested by a variety soliton equations.

The coherent-intermediate-entangled state |α, x⟩_λ,ν is proposed in the two-mode Fock Space, which exhibits both the properties of the coherent and entangled states. The |α,x⟩_λ,ν makes up a new quantum mechanical representation, and the completeness relation of |α,x⟩_λ,ν is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operators are derived. Furthermore, Generalized P-representation is constructed in the coherent-intermediate-entangled state |α,x⟩_λ,ν and the Schmidt decomposition of |α,x⟩_λ,ν is investigated.

The pseudospin symmetry in the Makarov potential is investigated systematically by solving the Dirac equation. The analytical solution for the Makarov potential with pseudospin symmetry is obtained by Nikiforov–Uvarov (N-U) method. The eigenfunctions and eigenenergies are presented with equal mixture of vector and scalar potentials in opposite signs, for which is exact.

The effect of Dzialoshinski–Moriya (DM) interaction on thermal entanglement of a two-qubit XXZ spin chain in a homogenous magnetic field is investigated. It is found that the DM interaction can enhance thermal entanglement. When D is large enough, the entanglement can exist for larger temperatures and strong magnetic field.

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrödinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well.

The effect of Dzialoshinski–Moriya (DM) interaction on thermal entanglement of an XY two-qutrit spin chain is investigated. We find that DM interaction and the anisotropy parameter can enhance quantum thermal entanglement to a maximal value individually. However, when both of them take large values, the entanglement is not enhanced, but is destroyed. Our analysis will shed some light on the understanding of the effect of the DM interaction on thermal entanglement of an XY two-qutrit spin chain.

By applying the Fourier slice theorem, , where P_θ(t) is a projection of along lines of constant, to the Wigner operator we are naturally led to a projection operator (pure state), which results in a new complete representation. The Weyl orderimg formalism of the Wigner operator is used in the derivation.

Nonlocal decoherence of two qubits due to pure phase damping has been investigated. We have proposed a scheme to keep the entanglement of two qubits from nonlocal decoherence. By applying a series of ±π pulses, nonlocal decoherence can be thoroughly suppressed.

We propose a simple scheme to not only generate GHZ states and W states of the multiparticle but also form a new category of multiparticle entangled states by letting the Λ-type three-level atoms simultaneously interacting with a coherent cavity field followed by the selective measurements on the cavity mode. We investigate the influence of the cavity dissipation on the generated entangled state and discuss the experimental feasibility of our scheme. It is shown that the intensity of the coherent cavity field plays an instructive role in contribution to state preparation process while the cavity decay and the detuning between the atoms and cavity mode result in the deterioration of the generated entangled state.

Based on the technique of integration within an ordered product of operators, the Weyl ordering operator formula is derived and the Fresnel operators' Weyl ordering is also obtained, which together with the Weyl transformation can immediately lead to Fresnel transformation kernel in classical optics.

We propose a quantum secure communication protocol by using three-particle GHZ states. In this protocol, we utilize the ideas of the rearranging orders and the sequence transmission. The sender of messages, Alice, first disturbs the particle orders in an initial sequence, and then sends the sequence of the disturbed orders to the receiver of messages, Bob. Under Alice's introduction, Bob rearranges the sequence back to the initial sequence. By making a GHZ state measurement on each of the three particles in turn, Bob can attain Alice's secret messages. In addition, we still calculate the efficiency of our three-particle GHZ protocol and generalize it to the case using multi-particle GHZ state.

We propose a scheme for multiparty-controlled remote preparation of the two-particle state by using two non-maximally Greenberger–Horne–Zeilinger states as quantum channel. Our scheme consists of one sender and n remote receivers. It will be shown that the sender can help either one of the n receivers to remotely preparation the original state with the appropriate probability, and the sender Alice's two-particle projective measurement and the controllers' single-particle product measurements are needed. We also obtained the probability of the successful remote state preparation.

A theoretical protocol of quantum dialogue is proposed, which uses a class of three-photon W states as quantum channel. After two-step security check, four-bit secret message can be transmitted to each other by transmitting of single photon with the aid of two-bit classical information.

This paper is devoted to investigating exact solutions of a generalized fractional nonlinear anomalous diffusion equation in radical symmetry. The presence of external force and absorption is also considered. We first investigate the nonlinear anomalous diffusion equations with one-fractional derivative and then multi-fractional ones. In both situations, we obtain the corresponding exact solutions, and the solutions found here can have a compact behavior or a long tailed behavior.

The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions (including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions) for the new (2+1)-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field.

In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spacetime. The tunneling effects lead to modified Hawking radiation due to inclusion of back-reaction effects. Our calculations show also that noncommutativity effects cause the further modifications to the thermodynamical relations in black hole. We calculate the emission rate of the massive particles' tunneling from a Schwarzschild black hole which is modified on account of noncommutativity influences. The issues of information loss and possible correlations between emitted particles are discussed. Unfortunately even by considering noncommutativity view point, there is no correlation between different modes of evaporation at least at late-time. Nevertheless, as a result of spacetime noncommutativity, information may be conserved by a stable black hole remnant.

In this paper, we study the phenomenon of stochastic resonance (SR) in a periodically driven bistable system with correlations between multiplicative and additive white noise terms when there are two different kinds of time delays existed in the deterministic and fluctuating forces, respectively. Using the small time delay approximation and the theory of signal-to-noise ratio (SNR) in the adiabatic limit, the expression of SNR is obtained. The effects of the delay time τ in the deterministic force, and the delay time θ in the fluctuating force on SNR are discussed. Based on the numerical computation, it is found that: (i) There appears a reentrant transition between one peak and two peaks and then to one peak again in the curve of SNR when the value of the time delay θ is increased. (ii) SR can be realized by tuning the time delay τ or θ with fixed noise, i.e., delay-induced stochastic resonance (DSR) exists.

A new image encryption approach is proposed. First, a sort transformation based on nonlinear chaotic algorithm is used to shuffle the positions of image pixels. Then the states of hyper-chaos are used to change the grey values of the shuffled image according to the changed chaotic values of the same position between the above nonlinear chaotic sequence and the sorted chaotic sequence. The experimental results demonstrate that the image encryption scheme based on a shuffling map shows advantages of large key space and high-level security. Compared with some encryption algorithms, the suggested encryption scheme is more secure.

We investigate the dynamics of a system coupled to an environment by averaged semiquantum method. The theory origins from the time-dependent variational principle (TDVP) formulation and contains nondiagonal matrix elements. So it can be applied to study dissipation, measurement, and decoherence problems in the model (H = h_S+h_E +h_I). In the calculation, the influence of the environment govern by differential dynamical equation is incorporated through a mean field. We have performed averaged semiquantum method for a spin-boson model, which reproduce the results from stochastic Schrodinger equation method and Hierarchical approach quite accurately. The problems, dynamics in nonequilibrium environments, have also been studied by our method.

With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrödinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have potential applications in the long-distance communication of two-pulse propagation in inhomogeneous optical fibers. Based on the obtained nonisospectral linear eigenvalue problems (i.e. Lax pair), we construct the Darboux transformation for such a model to derive the optical soliton solutions. In addition, through the one- and two-soliton-like solutions, we graphically discuss the features of picosecond solitons in inhomogeneous optical fibers.

We perform langevin dynamics simulation for envelope solitons in an FPU-β lattice, with the nearest-neighbor interaction and quartic anharmonicity. We get the motion equations of our discrete system by adding noise and damping to the set of deterministic motion equations. We define "half-time" as the time when the amplitude of the envelope soliton decreases by half due to damping. And then the mass, center and half-time of the perturbed envelope soliton are numerically simulated, beginning with the discrete envelope soliton at rest. Results show successfully how noise affects behavior of the envelope soliton.

Strong shock may induce complex processes in porous materials. We use the newly developed material-point-method to simulate such processes in an HMX-like material. To pick out relevant information, morphological characterization is used to treat with the temperature map. Via the Minkowski functional analysis the dynamics and thermodynamics of the shock wave reaction on porous HMX-like material are studied. The geometrical and topological properties of the "hot-spots" are revealed. Numerical results indicate that, shocks in porous materials are not simple jump states as classically viewed, but rather are a complex sequence of compressions and rarefactions. They cover a broad spectrum of states. We can use coarse-grained description to the wave series. A threshold value of temperature presents a Turing pattern dynamical procedure. A higher porosity is generally preferred when the energetic material needs a higher temperature for initiation. The technique of data analysis can be used to other physical quantities, for example, density, particle velocity, some specific stress, etc. From a series of studies along the line, one may get a large quantity of information for desiring the fabrication of material and choosing shock strength according to what needed is scattered or connected "hot-spots".

Adopting the approximation to the first order of chemical potential μ, we resolve rigidly the influence on fermion condensate from μ in QED₃. We show that this condensate does not respond linear expression to μ. Moreover, the influence on fermion chiral condensate from chemical potential is investigated.

This note concerns the motion of relativistic strings in the Minkowski space ¹⁺ⁿ. We rederive the general solution formula in closed form for the equation for the motion of relativistic string. Our method is different completely from others.

We study B_d → ϕK_S decay in extra down-type quarks (EDQS) model with a non-universal Z boson associated with flavor changing neutral currents (FCNCs) at the tree level. With the up-to-date experimental data of Br(B_d → ϕK_S), S_ϕKS, and A_ϕKS, we derive the bounds on the Z-b-s coupling parameter |U_bs| and the new weak phase ϕ, using the constrained parameter spaces, we finally give predictions for B_s → ϕϕ decay, which could be tested at the Fermilab Tevatron and the LHC-b experiments.

Close-coupling equation and anisotropic potential developed in our previous research are applied to HF-³He (⁴He, ⁶He, ⁸He, ¹⁰He) collision system, and partial cross sections (PCSs) at the incident energy of 40 meV are calculated. By analyzing the differences of these PCSs, change rules of PCSs with the increase of partial wave number, and with the change of the mass of isotope substitution helium atom are obtained. The results show that excitation PCSs converge faster than elastic PCSs for collision energy and each of systems considered here. Also excitation PCSs converge more rapidly for high-excited states. Tail effect is present only in elastic scattering and low-excited states but not in high-excited states. With the increase of the mass of isotope substitution helium atom, converging speed of elastic, total inelastic, and state-to-state excitation PCS slows down, and the maxima of these PCSs undergoes a regular change.

If a coherent perturbation field is used to couple the excited level of the coupling transition in the five-level K-type atom with another higher excited level, the two-photon electromagnetically induced transparency can be locally modulated by altering the parameters of the additional perturbation field. With different detunings of the coherent perturbation field, the absorption peak or transparency window with sharp and high-contrast spectral feature can be generated in the two-photon absorption spectrum. The physical interpretation of these phenomena is given in terms of the dressed states.

Based on the tortuous-expanding path/channel model, a micro-mechanism model for porous media is developed. The proposed model is expressed as a function of tortuosity, porosity, resistance coefficient, and fluid properties. Every parameter in the proposed model has clear physical meaning. The results show that the model predictions are in good agreement with those from the existing experimental data.

A Korteweg-de Vires-type (KdV-type) equation and a modified Nonlinear Schrödinger equation (NLSE) for the dust lattice wave (DLW) are derived in a weakly inhomogeneous dust plasma crystal. It seems that the amplitude and the velocity of the dust lattice solitary waves decay exponentially with increasing time in a dust lattice. The modulational instability of this dust lattice envelope waves is investigated as well. It is found that the waves are modulational stable under certain conditions. On the other hand, the waves are modulational unstable if the conditions are not satisfied.

We theoretically investigate the Kondo effect of a quantum dot embedded in a mesoscopic Aharonov–Bohm (AB) ring in the presence of the spin flip processes by means of the one-impurity Anderson Hamiltonian. Based on the slave-boson mean-field theory, we find that in this system the persistent current (PC) sensitively depends on the parity and size of the AB ring and can be tuned by the spin-flip scattering (R). In the small AB ring, the PC is suppressed due to the enhancing R weakening the Kondo resonance. On the contrary, in the large AB ring, with R increasing, the peak of PC firstly moves up to max-peak and then down. Especially, the PC phase shift of π appears suddenly with the proper value of R, implying the existence of the anomalous Kondo effect in this system. Thus this system may be a candidate for quantum switch.

We report a theoretic study on modulating the spin polarization of charge current in a mesoscopic four-terminal device of cross structure by using the inverse spin hall effect. The scattering region of device is a two-dimensional electron gas (2DEG) with Rashba spin orbital interaction (RSOI), one of lead is ferromagnetic metal and other three leads are spin-degenerate normal metals. By using Landauer–Büttiker formalism, we found that when a longitudinal charge current flows through 2DEG scattering region from FM lead by external bias, the transverse current can be either a pure spin current or full-polarized charge current due to the combined effect of spin hall effect and its inverse process, and the polarization of this transverse current can be easily controlled by several device parameters such as the Fermi energy, ferromagnetic magnetization, and the RSOI constant. Our method may pave a new way to control the spin polarization of a charge current.

The ground-state and lowest excited-state binding energies of a hydrogenic impurity in GaAs parabolic quantum-well wires (QWWs) subjected to external electric and magnetic fields are investigated using the finite-difference method within the quasi-one-dimensional effective potential model. We define an effective radius ρ_eff of a cylindrical QWW, which can describe the strength of the lateral confinement. For the ground state, the position of the largest probability density of electron in x-y plane is located at a point, while for the lowest excited state, is located on a circularity whose radius is ρ_eff. The point and circularity are pushed along the left half of the center axis of the quantum-well wire by the electric field directed along the right half. When an impurity is located at the point or within the circularity, the ground-state or lowest excited-state binding energies are the largest; when the impurity is apart from the point or circularity, the ground-state or lowest excited-state binding energies start to decrease.

Dependence of conductance of corrugated graphene quantum dot (CGQD) on geometrical features including length, width, connection and edge is investigated by the first principles calculations. The results demonstrate that the conductance of CGQD with different geometrical features is different from each other. The positions and amplitudes of discrete levels in densities of states and transmission coefficients are sensitive to geometrical features. The I-V characteristics of graphene are modified by size and edge, it is surprise the current does not change monotonously but oscillatory with length. And they are slight change for different connections.

The molecular-based magnetic materials AFe^IIFe^III (C₂O₄)₃ have a honeycomb structure in which Fe^II (S = 2) and Fe^III (S = 5/2) occupy sites alternately. They can be described as mixed spin-2 and spin-5/2 Ising model with ferrimagnetic interlayer coupling. The influences of the transverse field on the internal energy and the specific heat of the molecular-based magnetic system have been studied numerically by using the effective-field theory with self-spin correlations and the differential operator technique.

The specific heats of both a two-layer ferromagnetic superlattice and a two-layer ferrimagnetic one are studied. It is found that the spin quantum numbers, the interlayer and intralayer exchange couplings, the anisotropy, the applied magnetic field, and the temperature all affect the specific heat of these superlattices. For both the ferromagnetic and ferrimagnetic superlattices, the specific heat decreases with increasing the spin quantum number, the absolute value of interlayer exchange coupling, intralayer exchange coupling, and anisotropy, while it increases with increasing temperature at low temperatures. When an applied magnetic field is enhanced, the specific heat decreases in the two-layer ferromagnetic superlattice, while it is almost unchanged in the two-layer ferrimagnetic superlattice at low field range at low temperatures.

We present a short and direct derivation of Hawking radiation as a tunneling process across the horizon and compute the tunneling probability. Considering the self-gravitation and energy conservation, we use the Keskiy Vakkuri, Kraus, and Wilczek (KKW) analysis to compute the temperature and entropy of the black holes surrounded by quintessence and obtain the temperature and entropy are different from the Hawking temperature and the Bekenstein–Hawking entropy. The result we get can offer a possible mechanism to deal with the information loss paradox because the spectrum is not purely thermal.