The purpose of this paper is to introduce a class of generalized nonlinear evolution equations,which can be widely applied to describing a variety of phenomena in nonlinear physical science.A KdV-type Wronskian formulation is constructed by employing the Wronskian conditions of the KdV equation.Applications are made for the (3+1)-dimensional generalized KP,BKP and Jimbo-Miwa equations,thereby presenting their Wronskian sufficient conditions.An N-soliton solution in terms of Wronskian determinant is obtained.Under a dimensional reduction,our results yield Wronskian solutions of the KdV equation.

It is well known that soliton interactions in discrete integrable systems often possess new properties which are different from the continuous integrable systems,e.g.,we found that there are such discrete solitons in a semidiscrete integrable system (the time variable is continuous and the space one is discrete) that the shorter solitary waves travel faster than the taller ones.Very recently,this kind of soliton was also observed in a full discrete generalized KdV system (the both of time and space variables are discrete) introduced by Kanki et al.In this paper,for the generalized discrete KdV (gdKdV) equation,we describe its richer structures of one-soliton solutions.The interactions of two-soliton waves to the gdKdV equation are studied.Some new features of the soliton interactions are proposed by rigorous theoretical analysis.

The dark Korteweg-de Vries (KdV) systems are defined and classified by Kupershmidt sixteen years ago.However,there is no other classifications for other kinds of nonlinear systems.In this paper,a complete scalar classification for dark modified KdV (MKdV) systems is obtained by requiring the existence of higher order differential polynomial symmetries.Different to the nine classes of the dark KdV case,there exist twelve independent classes of the dark MKdV equations.Furthermore,for the every class of dark MKdV system,there is a free parameter.Only for a fixed parameter,the dark MKdV can be related to dark KdV via suitable Miura transformation.The recursion operators of two classes of dark MKdV systems are also given.

An invariant function (IF) is defined as a multiplier of a symmetry that means a symmetry multiplied by an IF is still a symmetry.Primary branch solutions of arbitrary first order scalar systems can be obtained by means of the IF and its related symmetry approach.Especially,one recursion operator and some sets of infinitely many high order symmetries are also explicitly given for arbitrary (1+1)-dimensional first order autonomous systems.Because of the intrusion of the arbitrary function,various implicit special exact solutions can be found by fixing the arbitrary functions and selecting different seed solutions.

We investigate the time evolution of quantum correlations of a hybrid qubit-qutrit system under the classical Ornstein-Uhlenbeck (OU) noise.Here we consider two different one-parameter families of qubit-qutrit states which independently interact with the non-Markovian reservoirs.A comparison with the Markovian dynamics reveals that for the same set of initial condition parameters,the non-Markovian behavior of the environment plays an important role in the enhancement of the survival time of quantum correlations.In addition,it is observed that the non-Markovian strength (γ/Γ) has a positive impact on the correlations time.For the initial separable states it is found that there is a finite time interval in which the geometric quantum discord is frozen despite the presence of a noisy environment and that interval can be further prolonged by using the non-Markovian property.Moreover,its decay can be significantly delayed.

It is first shown that the Dirac's equation in a relativistic frame could be modified to allow discrete time,in agreement to a recently published upper bound.Next,an exact self-adjoint 4×4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed.Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity,contrary to the general expectation from classical physics.Hence,Wolfgang Pauli's objection regarding the existence of a self-adjoint time operator is fully resolved.It is shown that using the time operator,a bosonic field referred here to as energons may be created,whose number state representations in non-relativistic momentum space can be explicitly found.

This paper investigates static axially symmetric models in self-interacting Brans-Dicke gravity.We discuss physically feasible sources of models,derive field equations as well as evolution equations from Bianchi identities and construct structure scalars.Using these scalars and evolution equations,the inhomogeneity factors of the system are evaluated.It is found that structure scalars related to double dual of Riemann tensor control the density inhomogeneity.Finally,we obtain exact solutions of homogenous isotropic and inhomogeneous anisotropic spheroid models.It turns out that homogenous solutions reduce to Schwarzschild type interior solutions for a spherical case.We conclude that homogenous models involve homogenous distribution of scalar field whereas inhomogeneous correspond to inhomogeneous scalar field.

In the present paper,we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations.The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as,the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEW),which are the important soliton equations.Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann-Liouville derivative.We plot the exact solutions for these equations at different time levels.

In this work,we perform a series of phonon counting measurement with different methods in a 3-mode optomechanical system,and we compare the difference of the Entanglment after measurement.In this article we focus on the three cases:prefect measurement,imperfect measurement and on-off measurement.We find that whatever measurement you take,the Entanglment will increase.The size of Entanglment enhancement is the largest in the perfect measurement,second in the imperfect measurement,and it is not obvious in the on-off measurement.We are sure that the more precise measurement information,the larger Entanglment concentration.

We study the entropy of Schwarzschild-de Sitter black holes based on generalized uncertainty principle with brick-wall method by counting degrees of freedom near the horizons and obtain the entropy proportional to the surface area at the horizons without cut-off.And reveal the possible value of the minimum length.

The gravitational collapse of a massless scalar field enclosed with a perfectly reflecting wall in a spacetime with a cosmological constant Λ is investigated.The mass scaling for the gapped collapse M_AH-M_g ∝(ε_c-ε)^ξ is confirmed and a new time scaling for the gapped collapse T_AH-T_g∝(ε_c-ε)^ζ is found.For both the critical exponents,we find strong evidence to show that they are non-universal.Especially when Λ≠0,we find that both of these two critical exponents depend on the combination Λ R²,where R is the radial position of the reflecting wall.We find an evolution of the critical exponent ξ from 0.37 in the confined asymptotic dS case with Λ R²=1.75 to 0.68 in the confined asymptotic AdS case with Λ R²=-1.75,while the critical exponent ζ varies from 0.10 to 0.26,which shows that the new critical behavior for the gapped collapse is essentially different from the Choptuik's case.

Amplifier is at the heart of experiments carrying out the precise measurement of a weak signal.An idea quantum amplifier should have a large gain and minimum added noise simultaneously.Here,we consider the quantum measurement properties of the cavity with the OPA medium in the op-amp mode to amplify an input signal.We show that our nonlinear-cavity quantum amplifier has large gain in the single-value stable regime and achieves quantum limit unconditionally.

The c-number atomic Bloch equations modelling the coupling of a 2-photon 2-level single atom with a non-resonant (△≠0) squeezed vacuum (SV) radiation reservoir show that:(i) The quantum interference (QI) process,of parameter f≠0,between the 2-photon transition channels causes coupling of the atomic variables (inversion and polarisation),and,(ii) The SV reservoir parameters (N,M) induce periodic coefficients and hence inhibited oscillatory behaviour in the atomic variables.Perturbative analytical solutions of these non-autonomous Bloch equations are derived and used to calculate the absorption spectrum of a weak field probing the system.Of particular,the zero-absorption isolines in the relevant (N,f)-and (△,f)-planes of the system parameters are identified computationally.It is found that,the largest set of points,where absorption is zero,in the (△,f)-plane depends on the choice of the degree of squeezing parameter (M) of the SV reservoir.

Heat transport phenomenon of two-dimensional magnetohydrodynamic Casson fluid flow by employing Cattaneo-Christov heat diffusion theory is described in this work.The term of heat absorption/generation is incorporated in the mathematical modeling of present flow problem.The governing mathematical expressions are solved for velocity and temperature profiles using RKF 45 method along with shooting technique.The importance of arising nonlinear quantities namely velocity,temperature,skin-friction and temperature gradient are elaborated via plots.It is explored that the Casson parameter retarded the liquid velocity while it enhances the fluid temperature.Further,we noted that temperature and thickness of temperature boundary layer are weaker in case of Cattaneo-Christov heat diffusion model when matched with the profiles obtained for Fourier's theory of heat flux.

The peristaltic flow of nanofluids is a relatively new area of research.Scientists are of the opinion that the no-slip conditions at the boundaries are no longer valid and consequently,the first and the second order slip conditions should be addressed.In this paper,the effects of slip conditions and the convective boundary conditions at the boundary walls on the peristaltic flow of a viscous nanofluid are investigated for.Also,the exact analytical solutions are obtained for the model.The obtained results are presented through graphs and discussed.The results reveal that the two slip parameters have strong effects on the temperature and the nanoparticles volume fraction profiles.Moreover,it has been seen that the temperature and nanoparticles volume fraction profiles attain certain values when the first slip condition exceeds a specified value.However,no limit value for the second slip parameter has been detected.Further,the effects of the various emerging parameters on the flow and heat transfer characteristics have been presented.

In this paper,a smooth repetitive oscillating wave traveling down the elastic walls of a non-uniform two-dimensional channels is considered.It is assumed that the fluid is electrically conducting and a uniform magnetic field is perpendicular to flow.The Sisko fluid is grease thick non-Newtonian fluid can be considered equivalent to blood.Taking long wavelength and low Reynolds number,the equations are reduced.The analytical solution of the emerging non-linear differential equation is obtained by employing Homotopy Perturbation Method (HPM).The outcomes for dimensionless flow rate and dimensionless pressure rise have been computed numerically with respect to sundry concerning parameters amplitude ratio φ,Hartmann number M,and Sisko fluid parameter b₁.The behaviors for pressure rise and average friction have been discussed in details and displayed graphically.Numerical and graphical comparison of Newtonian and non-Newtonian has also been evaluated for velocity and pressure rise.It is observed that the magnitude of pressure rise is maximum in the middle of the channel whereas for higher values of fluid parameter it increases.Further,it is also found that the velocity profile shows converse behavior along the walls of the channel against multiple values of fluid parameter.

The theory of dynamical (wake) potential behind a moving test charge in a weakly coupled dusty plasma is extended to that including of strong interaction between dust grains.Such strong interaction is included in the dielectric response function by a generalized hydrodynamic (GH) fluid model.It is shown that the strong interaction between dusts including the lattice spacing correction has a significant effect on the wake potential in dusty plasma.This may be used to investigate basic features of phase transition and possibility of lattice formation of dusty plasma.

The properties of dust ion acoustic waves are investigated in an unmagnetized multicomponent plasma system consisting of ion beam,charged positive and negative ions,electrons obeying nonthermal-Tsallis distribution and stationary negatively charged dust grains by the conventional Sagdeev pseudopotential method,through which the condition for existence of several nonlinear structures is analyzed theoretically.The dispersion relation for electrostatic waves is derived and analyzed and an expression of the energy integral equation is obtained.It is reported here that our plasma model supports solitions,double layers and supersoliton solutions for certain range of parameters.Finally,the effects of different physical plasma parameters on these nonlinear structures are studied numerically.The present theory should be helpful in understanding the salient features of the electrostatic waves in space and in laboratory plasmas where two distinct groups of ions and non-Maxwellian distributed electrons are present.

Electronic structures in two kinds of boron structures are investigated by the first-principle density functional theory (DFT) calculations.One structure is from theoretical prediction,and the other is from experimental investigation.Binding energy calculations suggest that the boron structure designed from theory is more stable than that made by experiment.Elastic constants calculations show that both structures are mechanically stable.The electronic structure results show that the theoretical designed structure exhibits semi-metal behavior,while the other structure exhibits metallic character.No magnetic phenomenal is discovered from them.All the calculations are carried out by the first principles calculation through the MatCloud platform,which is developed by our research group.

The different topological states of circular double-stranded DNA can be defined by their linking number.The equilibrium distribution of linking number can be obtained by circularizing a linear DNA into a circle by ligase.Based on the recent experimental results that the DNA bending rigidity and twist rigidity strongly depend on temperature,the reduced bending rigidity can be approximated by g=(3.19×10^-19-T·4.14×10^-22) erg·cm over the temperature interval (5~53)℃,and the temperature dependence of twist rigidity can be fitted by C (T)=(4588.89exp (-T/117.04)-251.33) nm.The temperature dependence of the linking number distribution of circular DNAs can be predicted by using Monte Carlo simulation.The variance of linking number distribution on temperature is in accordance with the previous experimental results.Compared with the temperature dependence of bending rigidity,the temperature dependence of twist rigidity causes a noticeable fluctuation in linking number distribution and mainly contribute towards the variance change of linking number distribution of circular DNA.The variance of the writhe number and twist number in the equation 〈(△ Lk)²〉=〈(△ Tw)²〉+〈(Wr)²〉 depends on the length of circular DNA.When the length of circular DNA is less than 230 nm,the variance of twist number 〈(△ Tw)²〉 is dominant over the variance of writhe number (〈(Wr)²〉),whereas for the condition that the length of the circular DNA is larger than 370 nm.

To understand how the stabilities of key nuclei fragments affect protein folding dynamics,we simulate by molecular dynamics (MD) simulation in aqueous solution four fragments cut out of a protein G,including one α-helix (seqB:KVFKQYAN),two β-turns (seqA:LNGKTLKG and seqC:YDDATKTF),and one β-strand (seqD:DGEWTYDD).The Markov State Model clustering method combined with the coarse-grained conformation letters method are employed to analyze the data sampled from 2-μs equilibrium MD simulation trajectories.We find that seqA and seqB have more stable structures than their native structures which become metastable when cut out of the protein structure.As expected,seqD alone is flexible and does not have a stable structure.Throughout our simulations,the native structure of seqC is stable but cannot be reached if starting from a structure other than the native one,implying a funnel-shape free energy landscape of seqC in aqueous solution.All the above results suggest that different nuclei have different formation dynamics during protein folding,which may have a major contribution to the hierarchy of protein folding dynamics.

In the present article, He's fractional derivative, the ansatz method, the (G'/G) -expansion method, and the exp-function method are used to construct the exact solutions of nonlinear space-time fractional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM). As a result, different types of exact solutions are obtained. Also we have examined the relation between the solutions obtained from the different methods. These methods are an efficient mathematical tool for solving fractional differential equations (FDEs) and it can be applied to other nonlinear FDEs.

We derive the Lax pair and Darboux transformation for the (2+1)-dimensional inhomogeneous Gardner equation via the two-singular manifold method from Painlevé analysis. N-soliton solution in a compact determinant representation of Grammian type is presented. As an application, dynamic properties of the bright and dark soliton solutions under periodic and parabolic oscillations up to second order are shown. Resonant behaviors of two bright and two dark solitons are studied, and asymptotic analysis of the corresponding resonant bright and dark two-soliton solutions are performed, respectively.

Applying the consistent Riccati expansion method, the extended (2+1)-dimensional shallow water wave equation is proved consistent Riccati solvable and the exact interaction solutions including soliton-cnoidal wave solutions, solitoff-typed solutions are obtained. With the help of the truncated Painlevé expansion, the corresponding nonlocal symmetry is also given, and furthermore, the nonlocal symmetry is localized by prolonging the related enlarged system.

Based on the bosonization approach, the supersymmetric Burgers (SB) system is transformed to a coupled bosonic system. By solving the bosonized SB (BSB) equation, the difficulties caused by the anticommutative fermionic field of the SB equation can be avoided. The nonlocal symmetry for the BSB equation is obtained by the truncated Painlevé method. By introducing multiple new fields, the finite symmetry transformation for the BSB equation is derived by solving the first Lie's principle of the prolonged systems. Some group invariant solutions are obtained with the similarity reductions related by the nonlocal symmetry.

A few important integrals involving the product of two universal associated Legendre polynomials P_l'^m'(x), P_k'^n'(x) and x^2a(1-x²)^-p-1, x^b(1±x)^-p-1 and x^c(1-x²)^-p-1(1±x) are evaluated using the operator form of Taylor's theorem and an integral over a single universal associated Legendre polynomial. These integrals are more general since the quantum numbers are unequal, i.e. l'≠k' and m'≠ n'. Their selection rules are also given. We also verify the correctness of those integral formulas numerically.

We develop generalized coherent states for a class of nonlinear oscillators with position-dependent effective mass in the context of the Gazeau-Klauder formalism and discuss some of their properties. In order to investigate the temporal evolution we first explore the statistical properties by means of weighting distribution and the Mandel parameter. It is found that the temporal evolution of the coherent states may exhibit the phenomena of quantum revivals and fractional revivals for a particular choice of position-dependent mass oscillator.

The developing tendency of continuous-variable (CV) measurement-device-independent (MDI) quantum cryptography is to cope with the practical issue of implementing scalable quantum networks. Up to now, most theoretical and experimental researches on CV-MDI QKD are focused on two-party protocols. However, we suggest a CV-MDI multipartite quantum secret sharing (QSS) protocol use the EPR states coupled with optical amplifiers. More remarkable, QSS is the real application in multipartite CV-MDI QKD, in other words, is the concrete implementation method of multipartite CV-MDI QKD. It can implement a practical quantum network scheme, under which the legal participants create the secret correlations by using EPR states connecting to an untrusted relay via insecure links and applying the multi-entangled Greenberger-Horne-Zeilinger (GHZ) state analysis at relay station. Even if there is a possibility that the relay may be completely tampered, the legal participants are still able to extract a secret key from network communication. The numerical simulation indicates that the quantum network communication can be achieved in an asymmetric scenario, fulfilling the demands of a practical quantum network. Additionally, we illustrate that the use of optical amplifiers can compensate the partial inherent imperfections of detectors and increase the transmission distance of the CV-MDI quantum system.

The security properties of quantum key distribution (QKD) system are analyzed with the practical light source using decoy state method. The secure key rate with the change of transmission distance is computed under the condition of ideal system, infinite light source system, untrusted light source and passive system. The influence of the fluctuation of transmission rate on the security characteristics of the system is discussed. Our numerical simulation results offer a useful reference for the practical QKD experiment.

Measurement-device-independent quantum key distribution (MDI-QKD) is immune to detector side channel attacks, which is a crucial security loophole problem in traditional QKD. In order to relax a key assumption that the sources are trusted in MDI-QKD, an MDI-QKD protocol with an untrusted source has been proposed. For the security of MDI-QKD with an untrusted source, imperfections in the practical experiment should also be taken into account. In this paper, we analyze the effects of fluctuations of internal transmittance on the security of a decoy-state MDI-QKD protocol with an untrusted source. Our numerical results show that both the secret key rate and the maximum secure transmission distance decrease when taken fluctuations of internal transmittance into consideration. Especially, they are more sensitive when Charlie's mean photon number per pulse is smaller. Our results emphasize that the stability of correlative optical devices is important for practical implementations.

A proposal for the generation of singlet states of three Λ-type Rydberg atoms is presented via the interaction between a separate Rydberg state and an EPR pair. Different from previous schemes, we do not need to couple ground states by using microwave lights but to set appropriate frequency detuning between lasers and two atomic transitions between ground states and Rydberg levels to eliminate the degenerate of the two ground states, making the present protocol more easily in experiment. Moreover, a series of numerical simulations are made to show the feasibility.

The coupled Gross-Pitaevskii equations for two-species BEC have been solved analytically under the Thomas-Fermi approximation (TFA). Based on the analytical solution, two formulae are derived to relate the particle numbers N_A and N_B with the root mean square radii of the two kinds of atoms. Only the case that both kinds of atoms have nonzero distribution at the center of an isotropic trap is considered. In this case the TFA has been found to work nicely. Thus, the two formulae are applicable and are useful for the evaluation of N_A and N_B.

In this paper, a model is proposed to solve the gauge hierarchy problem. Beyond the standard model, we introduce an extra scalar field that non-minimally couples to gravity. The fundamental scale is set at weak scale and Planck scale emerges dynamically by a spontaneous symmetry breaking mechanism.

The Hamiltonian analysis for a 3-dimensional connection dynamics of so(1,2), spanned by L_-+,L_-2,L₊₂ instead of L₀₁, L₀₂, L₁₂, is first conducted in a Bondi-like coordinate system. The symmetry of the system is clearly presented. A null coframe with 3 independent variables and 9 connection coefficients are treated as basic configuration variables. All constraints and their consistency conditions, the solutions of Lagrange multipliers as well as the equations of motion are presented. There is no physical degree of freedom in the system. The Bañados-Teitelboim-Zanelli (BTZ) spacetime is discussed as an example to check the analysis. Unlike the ADM formalism, where only non-degenerate geometries on slices are dealt with and the Ashtekar formalism, where non-degenerate geometries on slices are mainly concerned though the degenerate geometries may be studied as well, in the present formalism the geometries on the slices are always degenerate though the geometries for the spacetime are not degenerate.

We investigate the quantum dynamics of the decay of a multiple-component positronium condensate into pairs of photons. A positronium atom has four internal spin states which are interconvertible through s-wave interactions. The quantum fields of all spin states of positroniums and photons are simulated from first principle in quasi-one-dimensional system using the truncated Wigner method. This method warrants us a full treatment of the depletion of positronium fields and the spin mixing induced by s-wave collisions between positronium atoms. Particularly, it yields the momentum spectrum of the emitted photons and the photon-photon correlations.

This paper presents an investigation of weakly relativistic ponderomotive effects on self-focusing during interaction of high power elliptical laser beam with plasma. The nonlinear differential equations for the beam width parameters of elliptical laser beam have set up by using Wentzal-Krammers-Brillouin (WKB) and paraxial approximations. These equations have been solved numerically by using fourth order Runge-Kutta method to study the variation of these beam width parameters against normalized distance of propagation. Effects of variation in laser beam intensity, plasma density and electron temperature on the beam width parameters are also analyzed.

The present paper develops the scaling theory of polyelectrolyte nanogels in dilute and semidilute solutions. The dependencies of the nanogel dimension on branching topology, charge fraction, subchain length, segment number, solution concentration are obtained. For a single polyelectrolyte nanogel in salt free solution, the nanogel may be swelled by the Coulombic repulsion (the so-called polyelectrolyte regime) or the osmotic counterion pressure (the so-called osmotic regime). Characteristics and boundaries between different regimes of a single polyelectrolyte nanogel are summarized. In dilute solution, the nanogels in polyelectrolyte regime will distribute orderly with the increase of concentration. While the nanogels in osmotic regime will always distribute randomly. Different concentration dependencies of the size of a nanogel in polyelectrolyte regime and in osmotic regime are also explored.

We study the molecular state in three-component Fermi gases with a single impurity of ⁶Li immersing in a no-interacting Fermi sea of ⁴⁰K in the presence of an equal weight combination of Rashba-type and Dresselhaus-type spin-orbit coupling. In the region where the Fermi sea has two disjointed Fermi surfaces, we find that there are two Fulde-Ferrell-like molecular states with dominating contributions from the lower helicity branch. Decreasing the scattering length or the spin-orbit coupled Fermi energy, we find the Fulde-Ferrell-like molecular state with small center-of-mass momentum is always energy favored and the other one will suddenly disappear.

Using the first principles calculations based on density functional theory, the crystal structure, elastic anisotropy, and electronic properties of carbon, silicon and their alloys (C₁₂Si₄, C₈Si₈, and C₄Si₁₂) in a monoclinic structure (C2/m) are investigated. The calculated results such as lattice parameters, elastic constants, bulk modulus, and shear modulus of C₁₆ and Si₁₆ in C2/m structure are in good accord with previous work. The elastic constants show that C₁₆, Si₁₆, and their alloys in C2/m structure are mechanically stable. The calculated results of universal anisotropy index, compression and shear anisotropy percent factors indicate that C-Si alloys present elastic anisotropy, and C₈Si₈ shows a greater anisotropy. The Poisson's ratio and the B/G value show that C₈Si₈ is ductile material and other four C-Si alloys are brittle materials. In addition, Debye temperature and average sound velocity are predicted utilizing elastic modulus and density of C-Si alloys. The band structure and the partial density of states imply that C₁₆ and Si₁₆ are indirect band gap semiconductors, while C₁₂Si₄, C₈Si₈, and C₄Si₁₂ are semi-metallic alloys.

The problem of fragmentation (disintegration) process is theoretically studied with allowance for the initial particle volume. An exact analytical solution of integro-differential model governing the fragmentation phenomenon is obtained. The key role of a finite initial volume of particles leading to substantial changes of the particle-size distribution function is demonstrated.