The purpose of the present paper is twofold. First, the projective Riccati equations (PREs for short) are resolved by means of a linearized theorem, which was known in the literature. Based on the signs and values of coefficients of PREs, the solutions with two arbitrary parameters of PREs can be expressed by the hyperbolic functions, the trigonometric functions, and the rational functions respectively, at the same time the relation between the components of each solution to PREs is also implemented. Second, more new travelling wave solutions for some nonlinear PDEs, such as the Burgers equation, the mKdV equation, the NLS⁺ equation, new Hamilton amplitude equation, and so on, are obtained by using Sub-ODE method, in which PREs are taken as the Sub-ODEs. The key idea of this method is that the travelling wave solutions of nonlinear PDE can be expressed by a polynomial in two variables, which are the components of each solution to PREs, provided that the homogeneous balance between the higher order derivatives and nonlinear terms in the equation is considered.

The coupled higher-order nonlinear Schrödinger system is a major subject in nonlinear optics as one of the nonlinear partial differential equation which describes the propagation of optical pulses in optic fibers. By using coupled amplitude-phase formulation, a series of new exact cnoidal and solitary wave solutions with different parameters are obtained, which may have potential application in optical communication.

Three types of expression in the dark-soliton perturbation theory based on squared Jost solutions are investigated in this paper. It is shown that there are three formally different results about the effects of perturbation on a dark soliton, and it is proved by means of a transformation between two integral variables that they are essentially equivalent.

Firstly we expand a finite-dimensional Lie algebra into a higher-dimensional one. By making use of the later and its corresponding loop algebra, the expanding integrable model of the multi-component NLS-mKdV hierarchy is worked out.

The isospectral problem of the second mKdV equation is found out firstly. It follows that the strong hereditary symmetry and the Hamiltonian structure of the second mKdV equation are presented.

For a relativistic Birkhoffian system, the Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type are studied under general infinitesimal transformations. On the basis of the invariance of relativistic Birkhoffian equations under general infinitesimal transformations, Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The exact invariants in the form of generalized Hojman conserved quantities led by the Lie symmetries of relativistic Birkhoffian system without perturbations are given. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for relativistic Birkhoffian system with the action of small disturbance is investigated, and a new type of adiabatic invariants of the system is obtained. In the end of the paper, an example is given to illustrate the application of the results.

We present the continuous state vector of the total coordinate of multi-particle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product (IWOP) technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.

A simple barotropic potential vorticity equation with the influence of dissipation is applied to investigate the nonlinear Rossby wave in a shear flow in the tropical atmophere. By the reductive perturbation method, we derive the rotational KdV (rKdV for short) equation. And then, with the help of Jacobi elliptic functions, we obtain various periodic structures for these Rossby waves. It is shown that dissipation is very important for these periodic structures of rational form.

Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators (BEQPO's), we present the analytic expression of arbitrary matrix elements for BEQPO's. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO's.

We investigate the entanglement of formation for a class of high-dimensional quantum mixed states. We present a kind of generalized concurrence for a class of high-dimensional quantum pure states such that the entanglement of formation is a monotonically increasing convex function of the generalized concurrence. From the monotonicity and convexity the entanglement of formation for a class of high-dimensional mixed states has been calculated analytically.

A measuring-basis encrypted quantum key distribution scheme is proposed by using twelve nonorthogonal states in a four-state system and the measuring-basis encryption technique. In this scheme, two bits of classical information can be encoded on one four-state particle and the transmitted particles can be fully used.

A scheme for generating cluster states via Raman interaction is proposed. In the scheme, we firstly prepare cluster states of multi-cavities with information encoded in the coherent states and then generate cluster states of multi-atoms, which encode the information in the ground states of Λ-type atoms. The advantages of our scheme are that the atomic spontaneous radiation can be efficiently reduced since the cavity frequency is largely detuned from the atomic transition frequency and the Hadamard gate operation of the coherent states is replaced by measuring the coherent states.

We study a special two-atom entanglement case in assumed cavity QED experiment in which only one atom effectively exchanges a single photon with a cavity mode. We compute two-atom entanglement under position-dependent atomic resonant dipole-dipole interaction (RDDI) for large interatomic separation limit. We show that the RDDI, even that which is much smaller than the maximal atomic Rabi frequency, can induce distinct diatom entanglement. The peak entanglement reaches a maximum when RDDI strength can compare with the Rabi frequency of an atom.

Evolution of periodic waves and solitary waves in Bose-Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the mapping deformation method, we successfully obtain periodic wave solutions and solitary wave solutions, including the bright and dark soliton solutions. The results in this paper include some in the literatures [Phys. Rev. Lett. 94 (2005) 050402 and Chin. Phys. Lett. 22 (2005) 1855].

Motivated by the recently discovered hidden symmetry of the type IIB Green-Schwarz superstring on certain background, the non-semisimple Kac-Moody twisted superalgebra $\widehat{gl(2|2)^{(2)}}_k$ is investigated by means of the vector coherent state method and boson-fermion realization. The free field realization of the twisted current superalgebra at general level k is constructed. The corresponding Conformal Field Theory (CFT) has zero central charge. According to the classification theory, this CFT is a nonunitary field theory. After projecting out a U(1) factor and an outer automorphism operator, we get the free field representation of $\widehat{psl(2|2)^{(2)}}_k$, which is the algebra of $\widehat{gl(2|2)^{(2)}}_k$ modulo the Z₄-outer automorphism, the CFT has central charge -2.

The phase diagram of bulk quark matter in equilibrium with a finite hadronic gas is studied. Different from previous investigations, we treat the quark phase with the quark mass density-and-temperature-dependent model to take the strong quark interaction into account, while the hadron phase is treated by hard core repulsion factor. It is found that the phase diagram in this model is, in several aspects, different from those in the conventional MIT bag model, especially at high temperature. The new phase diagram also has strong effects on the mass-radius relation of compact hybrid stars.

Based on the φ-mapping topological current theory and the decomposition of gauge potential theory, we investigate knotted vortex lines and monopoles in Skyrme theory and simply discuss the branch processes (splitting, merging, and intersection) during the evolution of the monopoles.

The formalisms of helicity coupling amplitudes for J/ψ → π⁺π^-π⁰ are presented. A detailed discussion is also given on the barrier factor, Breit-Wigner, and density matrix. A Monte-Carlo simulation of J/ψ → ρ(770)π → π⁺π^-π⁰ is carried out. The results show that the ρ(770) resonance is well reproduced compared with experimental data.

By means of a relativistic effective potential, we analytically research competition between the quark-antiquark condensates〈qq〉and the diquark condensates 〈qq〉 in vacuum in ground state of a two-flavor Nambu-Jona-Lasinio (NJL) model and obtain the G_S-H_S phase diagram, where G_S and H_S are the respective four-fermion coupling constants in scalar quark-antiquark channel and scalar color anti-triplet diquark channel. The results show that, in the chiral limit, there is only the pure 〈qq〉 phase when G_S/H_S>2/3, and as G_S/H_S decreases to 2/3>G_S/H_S≥0 one will first have a coexistence phase of the condensates〈qq〉and 〈qq〉and then a pure〈qq〉phase. In non-zero bare quark mass case, the critical value of G_S/H_S at which the pure 〈qq〉phase will transfer to the coexistence phase of the condensates 〈qq〉and 〈qq〉will be less than 2/3. Our theoretical results, combined with present phenomenological fact that there is no diquark condensates in the vacuum of QCD, will also impose a real restriction to any given two-flavor NJL model which is intended to simulate QCD, i.e. in such model the resulting smallest ratio G_S/H_S after the Fierz transformations in the Hartree approximation must be larger than 2/3. A few phenomenological QCD-like NJL models are checked and analyzed.

A new light nuclear reaction model has been developed and the double-differential measurements of 1p shell nuclei have been analyzed successfully. Now, the application of this model is expanded to ¹⁹F of the 2s-1d shell nucleus. The double-differential cross section of total outgoing neutron for n+¹⁹F reactions at E_n=14.2 MeV has been calculated and analyzed, which agrees fairly well with the experimental measurements. In this paper, the contributions from different reaction channels to the double-differential cross sections have been analyzed in detail. The calculations indicate that this light nuclear reaction model is also able to be used for the 2s-1d shell nucleus so long as the related level scheme could be provided sufficiently.

Based on the Ward-Takahashi identity at finite chemical potential and Lorentz structure analysis, we generalize the Ball-Chiu vertex to the case of nonzero chemical potential and obtain the general form of the fermion-boson vertex in QED at finite chemical potential.

Antikaon condensation and kaon and antikaon production in protoneutron stars are investigated in a chiral hadronic model (also referred to as the FST model in this paper). The effects of neutrino trapping on protoneutron stars are analyzed systematically. It is shown that neutrino trapping makes the critical density of K^- condensation delay to higher density and K⁰ condensation not occur. The equation of state (EOS) of (proto)neutron star matter with neutrino trapping is stiffer than that without neutrino trapping. As a result, the maximum masses of (proto)neutron stars with neutrino trapping are larger than those without neutrino trapping. If hyperons are taken into account, antikaon does not form a condensate in (proto)neutron stars. Meanwhile, the corresponding EOS becomes much softer, and the maximum masses of (proto)neutron stars are smaller than those without hyprons. Finally, our results illustrate that the Q values for K⁺ and K^- production in (proto)neutron stars are not sensitive to neutrino trapping and inclusion of hyperons.

The B-spline expansion technique is applied to study the anticrossings for potassium Rydberg states in a static electric field. The results of our calculation indicate that the anticrossings are caused mainly by the core interaction or by the fine structure interaction. Our results for the positions and the widths of the anticrossings are in good agreement with experimental data.

For an atom in a medium with refractive index n sandwiched between two parallel mirrors, we derive an analytical formula for the spontaneous emission rate based on Fermi's golden rule. The oscillations are not transparent in this formula. By performing Fourier transform on scaling variable measuring system size while holding system configuration fixed, we extracted the frequencies of many oscillations in this system. We show that these oscillations correspond to emitted photon closed-orbits going away from and returning to the emitting atom.

The cavity field spectrum of a cascade three-level atom interacting with single-mode field with Kerr-like medium in the cavity is investigated. The numerical results for the initial field in pure number state, coherent state and squeezed vacuum state are calculated, respectively. It is found that the Kerr-like medium affects the spectral structure even though the initial field is in vacuum when the atom is in upper level. In the case of strong input field, the number state spectrum shows two peaks with different heights; and the superposition state spectrum shows a multi-peak structure with an equal distance of two neighboring peaks. The spectral “central frequency” shifts away from the resonant frequency with the increasing of average photon number.

By virtue of the technique of integration within an ordered product of operators a new four-mode squeezing operator that squeezes the four-mode quadrature operators of light field in the standard way is found. This operator differs from the direct product of two two-mode squeezing operators. It is the exponential operator V≡exp[ir(Q₁P₂+Q₂P₃+Q₃P₄+Q₄P₁)]. The Wigner function of the new four-mode squeezed state is calculated, which quite differs from that of the direct-product state of two usual two-mode squeezed states.

By virtue of the properties of bipartite entangled state representation we derive the common eigenvector of the parametric Hamiltonian and the two-mode number-difference operator. This eigenvector is superposition of some definite two-mode Fock states with the coefficients being proportional to hypergeometric functions. The Gauss contiguous relation of hypergeometric functions is used to confirm the formal solution.

In the paper, the generalized Riccati equation rational expansion method is presented. Making use of the method and symbolic computation, we present three families of exact analytical solutions of Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Then the dynamics of two anlytical solutions are demonstrated by computer simulations under some selectable parameters including the Feshbach-managed nonlinear coefficient and the hyperbolic secant function coefficient.

A modified Zakharov-Kuznetsov equation for small but finite amplitude dust acoustic waves in a magnetized votex-like ion distribution dusty plasma is obtained in this paper. It seems that there are instability for a soliton under higher-order transverse perturbations in this system. There is a certain critical value 4λ₀. If the ratio of the wave length of the higher-order perturbations to the width of the soliton is larger than this critical value, the solitary wave is unstable, otherwise it is stable.

A spherical Kadomtsev-Petviashvili (SKP) equation for dust acoustic or ion-acoustic waves is studied. Similarity reductions of the SKP equation are obtained with the one-parameter Lie group of infinitesimal transformations and Clarkson-Kruskal direct method. The SKP equation is also solved with a generalized tanh function method.

We present a comparative study of the ground state of the one-dimensional Hubbard model. We first use a new fermion coherent state method in the framework of Fermi liquid theory by introducing a hole operator and considering the interactions of two pairs electrons and holes. We construct the ground state of the Hubbard model as |>=[f+∑'φ c_k1σ1 ^† h_k2σ2 ^† c_k3σ3 ^† h_k4σ4 ^† ∏exp(ρc_k1σ1 ^† h_k2σ2 ^†)]|>₀, where φ and ρ are coupling constants. Our results are then compared to those of variational methods, density functional theory based on the exact solvable Bethe ansatz solutions, variational Monto-Carlo method (VMC) as well as to the exact result of the infinite system. We find satisfactory agreement between the fermion coherent state scheme and the VMC data, and provide a new picture to deal with the strongly correlated system.

We study a neutral donor center (D⁰) and a negatively charged donor center (D^-) trapped by a quantum dot, which is subjected to a Gaussian potential confinement. Calculations are made by using the method of numerical diagonalization of Hamiltonian within the effective-mass approximation. The dependence of the ground state of the neutral shallow donor and the negatively charged donor on the dot size and the potential depth is investigated. The same calculations performed with the parabolic approximation of the Gaussian potential lead to the results that are qualitatively and quantitatively different from each other.

In the present paper, we investigate the quantum phase transition in a spatially anisotropic antiferromagnetic Heisenberg model of S=1 with single-ion energy anisotropy. By using the Schwinger boson representation, we calculate the Gaussian correction to the critical value J_⊥^c caused by quantum spin fluctuations. We find that, for the positive single-ion energy, a nonzero value of J_⊥^c is always needed to stabilize the antiferromagnetic long-range order in this model. It resolves a difference among literature and shows clearly that the effect of quantum fluctuations may qualitatively change a result obtained by the mean-field theories on lower-dimensional systems.

We study a three-dimensional off-lattice protein folding model, which involves two species of residues interacting through Lennard-Jones potentials. By incorporating an extra energy contribution into the original potential function, we replace the original constrained problem with an unconstrained minimization of a mixed potential function. As such an efficient quasi-physical algorithm for solving the protein folding problem is presented. We apply the proposed algorithm to sequences with up to 55 residues and compare the computational results with the putative lowest energy found by several of the most famous algorithms, showing the advantages of our method. The dynamic behavior of the quasi-physical algorithm is also discussed.

This paper proposes a novel complex network with assortative property based on multi-center networks. The average path length and clustering coefficient of the network are calculated, and the impact on the network topology is investigated. A simple dynamic system established on the proposed network is used to analyze how the assortative property of the network affects synchronization.

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.