Table of contents

We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term: u_t = (A(x)D(u)u_x)_x+B(x)Q(u), A_x≠0. The functional separation of variables to this equation is studied by using the group foliation method. A classification is carried out for the equations which admit the function separable solutions. As a consequence, some solutions to the resulting equations are obtained.

In this paper, a new extended complex tanh-function method is presented for constructing traveling wave, non-traveling wave, and coefficient functions' soliton-like solutions of nonlinear equations. This method is more powerful than the complex tanh-function method [Chaos, Solitons and Fractals 20 (2004) 1037]. Abundant new solutions of (2+1)-dimensional Hirota equation are obtained by using this method and symbolic computation system Maple.

Though the Bäcklund transformation on time-like surfaces with constant mean curvature surfaces in R^2,1 has been obtained, it is not easy to obtain corresponding surfaces because the procedure of solving the related integrable system cannot be avoided when the Bäcklund transformation is used. For sake of this, in this article, some special work is done to reform the Bäcklund transformation to a recursion formula, by which we can construct time-like surfaces with constant mean curvature form known ones just by quadrature procedure.

Routh order reduction method of the relativistic Birkhoffian equations is studied. For a relativistic Birkhoffian system, the cyclic integrals can be found by using the perfect differential method. Through these cyclic integrals, the order of the system can be reduced. If the relativistic Birkhoffian system has a cyclic integral, then the Birkhoffian equations can be reduced at least by two degrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics, and the relativistic Lagrangian mechanics are discussed, and the Routh order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of the result.

The paper studies the form invariance and a type of non-Noether conserved quantity called Mei conserved quantity for non-holonomic systems with variable mass and unilateral constraints. Acoording to the invariance of the form of differential equations of motion under infinitesimal transformations, this paper gives the definition and criterion of the form invariance for non-holonomic systems with variable mass and unilateral constraints. The condition under which a form invariance can lead to Mei conservation quantity and the form of the conservation quantity are deduced. An example is given to illustrate the application of the results.

The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integrating factors is given, and the necessary conditions for the existence of the conserved quantities are studied in detail. Then, the conservation theorem and its inverse of system are established. Finally, an example is given to illustrate the application of the result.

The unified symmetry of a nonholonomic system of non-Chetaev's type in event space under infinitesimal transformations of group is studied. Firstly, the differential equations of motion of the system are given. Secondly, the definition and the criterion of the unified symmetry for the system are obtained. Thirdly, a new conserved quantity, besides the Noether conserved quantity and the Hojman conserved quantity, is deduced from the unified symmetry of a nonholonomic system of non-Chetaev's type. Finally, an example is given to illustrate the application of the result.

This paper suggests a systematic method based on supersymmetric quantum mechanics for generating conditionally exactly soluble potentials, and uses the variational supersymmetric WKB method to obtain the approximate values of the energy spectrum of the whole class.

We revisit the quantum decoherence problem of the center of mass motion of a macroscopic object, which is modelled as a one-dimensional atom chain. Induced by the coupling of the center of mass (C.M) motion with the inner degrees of freedom, this inner-environment-induced decoherence is reflected by the localization of the C.M wave packet. We show that, the C.M motion is coupled to the inner states only when the chain has interaction with the external potential. This result provides a realistic mechanism for the analysis of the inner-environment-induced localization of a macroscopic object.

The dynamic properties of proton conductivity along hydrogen-bonded molecular systems, for example, ice crystal, with structure disorder or damping and finite temperatures exposed in an externally applied electric-field have been numerically studied by Runge–Kutta way in our soliton model. The results obtained show that the proton-soliton is very robust against the structure disorder including the fluctuation of the force constant and disorder in the sequence of masses and thermal perturbation and damping of medium, the velocity of its conductivity increases with increasing of the externally applied electric-field and decreasing of the damping coefficient of medium, but the proton-soliton disperses for quite great fluctuation of the force constant and damping coefficient. In the numerical simulation we find that the proton-soliton in our model is thermally stable in a large region of temperature of T⩽273 K under influences of damping and externally applied electric-field in ice crystal. This shows that our model is available and appropriate to ice.

We propose an experimentally feasible scheme for implementing quantum restoring machine of the optimal universal 1→2 quantum cloning machine in the context of cavity QED. In our scheme, two atoms (the clones) simultaneously interact with a cavity field, and meanwhile they are driven by a classical field. Then an arbitrary unknown input state can be restored in the ancilla by applying appropriate unitary local operation.

We propose a scheme to remotely prepare a general two-particle entangled state by using a bipartite entangled state and a tripartite entangled W state as the quantum channel. Our scheme consists of one sender and two remote receivers. The sender can help either one of the receivers to remotely reconstruct the original state with the assistance of the other receiver's single-particle orthogonal measurement. We obtain the total success probability and discuss the classical communication cost in our remote state preparation scheme.

A scheme for approximately and conditionally teleporting an unknown atomic-entangled state in cavity QED is proposed. It is the novel extension of the scheme of [Phys. Rev. A 69 (2004) 064302], where the state to be teleported is an unknown atomic state and where only a time point of system evolution and the corresponding fidelity implementing the teleportation are given. In fact, there exists multi-time points and the corresponding fidelities, which are shown in this paper and then are used to realize the approximate and conditional teleportation of the unknown atomic-entangled state. Naturally, our scheme does not involve the Bell-state measurement or an additional atom, which is required in the Bell-state measurement, only requiring one single-mode cavity. The scheme may be generalized to not only the teleportation of the cavity-mode-entangled-state by means of a single atom but also the teleportation of the unknown trapped-ion-entangled-state in a linear ion trap and the teleportation of the multi-atomic entangled states included in generalized GHZ states.

We present a theoretical scheme for perfect teleportation of an unknown multipartite two-level state by a single EPR (Einstein–Podolsky–Rosen) pair, and then generalize it to multilevel, i.e., an N-quNit state can be teleported by a single quNit entangled pair, with additional local unitary operations. The feature of the scheme is that teleporting a multipartite state with a reduced amount of entanglement costs less classical bits.

When a Bose–Einstein condensate is set to rotate, superfluid vortices will be formed, which finally condense into a vortex lattice as the rotation frequency further increases. We show that the dipole-dipole interactions renormalize the short-range interaction strength and result in a distinction between interactions of parallel-polarized atoms and interactions of antiparallel-polarized atoms. This effect may lead to a spontaneous breakdown of the rapidly rotating Bose condensate into a novel anti-ferromagnetic-like vortex lattice. The upward-polarized Bose condensate forms a vortex lattice, which is staggered against a downward-polarized vortex lattice. A phase diagram related to the coupling strength is obtained.

Phase synchronization of two linearly coupled Rossler oscillators with parameter misfits is explored. It is found that depending on parameter mismatches, the synchronization of phases exhibits different manners. The synchronization regime can be divided into three regimes. For small mismatches, the amplitude-insensitive regime gives the phase-dominant synchronization; When the parameter misfit increases, the amplitudes and phases of oscillators are correlated, and the amplitudes will dominate the synchronous dynamics for very large mismatches. The lag time among phases exhibits a power law when phase synchronization is achieved.

In this paper, by using symbolic and algebra computation, Chen and Wang's multiple Riccati equations rational expansion method was further extended. Many double soliton-like and other novel combined forms of exact solutions of the (2+1)-dimensional Breaking soliton equation are derived by using the extended multiple Riccati equations expansion method.

With the aid of an improved projective approach and a linear variable separation method, new types of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (2+1)-dimensional Korteweg-de Vries system are derived. Usually, in terms of solitary wave solutions and rational function solutions, one can find some important localized excitations. However, based on the derived periodic wave solution in this paper, we find that some novel and significant localized coherent excitations such as dromions, peakons, stochastic fractal patterns, regular fractal patterns, chaotic line soliton patterns as well as chaotic patterns exist in the KdV system as considering appropriate boundary conditions and/or initial qualifications.

Using extended homogeneous balance method and variable separation hypothesis, we found new variable separation solutions with three arbitrary functions of the (2+1)-dimensional dispersive long-wave equations. Based on derived solutions, we revealed abundant oscillating solitons such as dromion, multi-dromion, solitoff, solitary waves, and so on, by selecting appropriate functions.

In this article, we study the structures of the pseudoscalar mesons π, K and the scalar diquarks U^a, D^a, S^a in the framework of the coupled rainbow Schwinger–Dyson equation and ladder Bethe–Salpeter equation with the confining effective potential. The u, d, s quarks have small current masses, and the renormalization is very large, the mass poles in the timelike region are absent which implements confinement naturally. The Bethe–Salpeter wavefunctions of the pseudoscalar mesons π, K, and the scalar diquarks U^a, D^a, S^a have the same type (Gaussian type) momentum dependence, center around zero momentum and extend to the energy scale about q² = 1 GeV², which happens to be the energy scale for the chiral symmetry breaking, the strong interactions in the infrared region result in bound (or quasi-bound) states. The numerical results for the masses and decay constants of the π and K mesons can reproduce the experimental values, and the ground state masses of the scalar diquarks U^a, D^a, S^a are consistent with the existing theoretical calculations. We suggest a new Lagrangian which may explain the uncertainty of the masses of the scalar diquarks.

By differentiating the dressed quark propagator with respect to a variable background field, the linear response of the dressed quark propagator in the presence of the background field can be obtained. From this general method, using the vector background field as an illustration, we extract a general formula for the four-quark condensate ⟨|:(0)γ_μq(0)(0)γ_μq(0):|⟩. This formula contains the corresponding fully dressed vector vertex. We use this formula to analyze the factorization problem of the four-quark condensate and show that in the bare vertex approximation factorization holds exactly.

We study the rare radiative dileptonic decays B⁰(B_s)→γℓ⁺ℓ⁻ (ℓ = e,μ) in the standard model. By using the B meson wave function constrained by non-leptonic decays, the branching ratios turn out to be of the order of 10⁻⁹ for B_s→γμ⁺μ⁻, γe⁺e⁻, and 10⁻¹⁰ for B⁰→γμ⁺μ⁻, γe⁺e⁻. Based on the study, these decays are accessible at the near future LHC-b experiment, which are useful to determine the B(B_s) wave function.

The level density parameter and the back shift energy E₁ are determined for nuclei with A-values across the whole periodic table from fits to complete level schemes at low excitation energy near the neutron binding energies. We find that the energy back shift E₁ shows complicated behavior and depends on the type of the nucleus, even-even, odd mass, and odd-odd. The spin cut-off factor has also been investigated for nuclei mentioned above. The results are compared with the previous results and different experimental data on level densities.

The collective Hamiltonian up to the fourth order for multi-O(4) model is derived based on the self-consistent collective-coordinate (SCC) method, which is formulated in the framework of the time-dependent Hartree–Bogoliubov (TDHB) theory. The validity of the collective Hamiltonian is checked in the two special cases of the multi-O(4) model: the case where the number of the shells is equal to one (a single j-shell case), and the case where the Hartree–Bogoliubov equilibrium point is spherical (the spherical case). The collective Hamiltonian constitutes a good starting point to study nuclear shape coexistence.

Two new types of quantum states are constructed by applying the operator s(ξ) = exp (ξ*ab−ξa^†b^†) on the two-mode even and odd coherent states. The mathematical and quantum statistical properties of such states are investigated. Various nonclassical features of these states, such as squeezing properties, the inter-mode photon bunching, and the violation of Cauchy–Schwarz inequality, are discussed. The Wigner function in these states are studied in detail.

We introduce the coordinate-dependent two-mode squeezing transformations and discuss the properties of the corresponding two-mode squeezed states.

A scheme is reported for the teleportation of entangled coherent states through the degenerate Raman interaction. The scheme uses an entangled state of an atom and two coherent states as a quantum channel. It makes full use of coherent cavity fields. Furthermore, it does not need any classical field to transform the atom states.

For ion-acoustic waves in a plasma with non-isothermal electrons, the MKP equation is its governing equation. The instability of a soliton solution of MKP equation to two-dimensional long-wavelength perturbations is investigated up to the third order. It indicates that the one-soliton solution of MKP equation is unstable if ν = −1 wheras it is stable if ν = 1 until the third order approximation has been considered.

In this paper, (2+1)-dimensional electron acoustic waves (EAW) in an unmagnetized collisionless plasma have been studied by the linearized method and the reductive perturbation technique, respectively. The dispersion relation and a modified Kadomtsev–Petviashvili (KP) equation have been obtained for the EAW in the plasma considering a cold electron fluid and a vortex-like hot electrons. It is found from some numerical results that the parameter β (the ratio of the free hot electron temperature to the hot trapped electron temperature) effects on the amplitude and the width of the electron acoustic solitary waves (EASW). It can be indicated that the free hot electron temperature and the hot trapped electron temperature have very important effect on the characters of the propagation for the EASW.

This paper gives methods to calculate the pairing temperature T*, at which a pseudogap is opened, and the superconducting temperature T_c, at which superconductivity appears, in the high-T_c cuprates, and demonstrates directly that at T_c<T<T* the pseudogap is the gap of Cooper pair without long-range phase coherence, and at T<T_c there is long-range phase coherence between Cooper pairs. Based on the above clear physical picture on the pseudogap state and our mechanism for the ac Josephson effect, this paper proposes that there should be a novel oscillatory current in P-I-P junction, induced by a constant bias on the junction. Here, P represents the high-T_c curates in the pseudogap state, where Cooper pairs do not have long-range phase coherence, and I represents the thin insulating barrier. This paper conjectures that there is a possible high-temperature superconductivity in the heavily underdoped high-T_c cuprates.

Based on the dielectric continuum model and Loudon's uniaxial crystal model, the properties of the quasi-confined (QC) optical phonon dispersions and the electron-QC phonons coupling functions in an asymmetric wurtzite quantum well (QW) are deduced via the method of electrostatic potential expanding. The present theoretical scheme can naturally reduce to the results in symmetric wurtzite QW once a set of symmetric structural parameters are chosen. Numerical calculations on an asymmetric AlN/GaN/Al_0.15Ga_0.85N wurtzite QW are performed. A detailed comparison with the symmetric wurtzite QW was also performed. The results show that the structural asymmetry of wurtzite QW changes greatly the dispersion frequencies and the electrostatic potential distributions of the QC optical phonon modes.

We propose a novel two-species aggregation-annihilation model, in which irreversible aggregation reactions occur between any two aggregates of the same species and biased annihilations occur simultaneously between two different species. The kinetic scaling behavior of the model is then analytically investigated by means of the mean-field rate equation. For the system without the self-aggregation of the un-annihilated species, the aggregate size distribution of the annihilated species always approaches a modified scaling form and vanishes finally; while for the system with the self-aggregation of the un-annihilated species, its scaling behavior depends crucially on the details of the rate kernels. Moreover, the results also exhibit that both species are conserved together in some cases, while only the un-annihilated species survives finally in other cases.

In the paper, we study effects of scale-free (SF) topology on dynamical synchronization and control in coupled map lattices (CML). Our strategy is to apply three feedback control methods, including constant feedback and two types of time-delayed feedback, to a small fraction of network nodes to reach desired synchronous state. Two controlled bifurcation diagrams verses feedback strength are obtained respectively. It is found that the value of critical feedback strength γ_c for the first time-delayed feedback control is increased linearly as ε is increased linearly. The CML with SF loses synchronization and intermittency occurs if γ>γ_c. Numerical examples are presented to demonstrate all results.

In this paper, we propose a new model of weighted small-world biological neural networks based on biophysical Hodgkin–Huxley neurons with side-restrain mechanism. Then we study excitement properties of the model under alternating current (AC) stimulation. The study shows that the excitement properties in the networks are preferably consistent with the behavior properties of a brain nervous system under different AC stimuli, such as refractory period and the brain neural excitement response induced by different intensities of noise and coupling. The results of the study have reference worthiness for the brain nerve electrophysiology and epistemological science.

An analytical expression for the jet power extracted from the plunging region between a black hole (BH) horizon and the inner edge of the disk (hereafter the PL power) is derived based on an improved equivalent circuit in BH magnetosphere with a mapping relation between the radial coordinate of the plunging region and that of the remote astrophysical load. It is shown that the PL power is of great importance in explaining jet power and dominates over the BZ and DL powers for a wide value range of the BH spin. In addition, we show that the PL power derived in our model can be fitted with the strong jet powers of several 3CR FR I radio galaxies, which cannot be explained by virtue of the BZ mechanism. Furthermore, the condition for negative energy of the accreting particles in the plunging region is discussed with the validity of the second law of BH thermodynamics.

The universe content is considered as a non-perfect fluid with bulk viscosity and is described by a more general equation of state (endowed some deviation from the conventionally assumed cosmic perfect fluid model). We assume the bulk viscosity is a linear combination of two terms: one is constant, and the other is proportional to the scalar expansion θ = 3/a. The equation of state is described as p = (γ−1)ρ+p₀, where p₀ is a parameter. In this framework we demonstrate that this model can be used to explain the dark energy dominated universe, and different proper choices of the parameters may lead to three kinds of fates of the cosmological evolution: no future singularity, big rip, or Type-III singularity as presented in [S. Nojiri, S.D. Odintsov, and S. Tsujikawa, Phys. Rev. D 71 (2005) 063004].