Multi-soliton solutions, breather-like and bound-state solitons for complex modified Korteweg–de Vries equation in optical fibers

Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained through the Hirota method and symbolic computation. Breather-like and bound-state solitons are constructed in which the signs of the imaginary parts of the complex wave numbers and the initial separations of the two parallel solitons are important factors for the interaction patterns. The periodic structures and position-induced phase shift of some solutions are introduced.

Exact Solutions of Klein-Gordon Equation with Scalar and Vector Rosen-Morse-Type Potentials

We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by using the asymptotic iteration method. Although these PT symmetric potentials are non-Hermitian, the corresponding eigenvalues are real as a result of the PT symmetry.

Exact Solutions of the Klein-Gordon Equation with a New Anharmonic Oscillator Potential

We solve the Klein-Cordon equation with a new anharmonic oscillator potential and present the exact solutions. It is shown that under the condition of equal scalar and vector potentials, the Klein-Cordon equation could be separated into an angular equation and a radial equation. The angular solutions are the associated-Legendre polynomial and the radial solutions are expressed in terms of the confluent hypergeometric functions. Finally, the energy equation is obtained from the boundary condition satisfied by the radial wavefunctions.

Investigation of Dilaton-Gluon Coupling Potential in Charmonium Family

The behaviour of dilaton-gluon coupling （DGC） potential is investigated by studying charmonium spectra, annihilation rates and E1 transition rates systematically. We find that in the non-relativistic quantum chromodynamics approximation, the charmonium properties can be described by the DGC potential.

Exact Solution of Klein-Gordon Equation by Asymptotic Iteration Method

Using the asymptotic iteration method （AIM） we obtain the spectrum of the Klein-Gordon equation for some choices of scalar and vector potentials. In particular, it is shown that the AIM exactly reproduces the spectrum of some solvable potentials.

Potential Energy Surfaces of Nitrogen Dioxide for the Ground State

The potential energy function of nitrogen dioxide with the C2v symmetry in the ground state is represented using the simplified Sorbie-Murrell many-body expansion function in terms of the symmetry of NO2. Using the potential energy function, some potential energy surfaces of NO2（C2v, X^-^2A1）, such as the bond stretching contour plot for a fixed equilibrium geometry angle θ and contour for O moving around N-O （R1）, in which R1 is fixed at the equilibrium bond length, are depicted. The potential energy surfaces are analysed. Moreover, the equilibrium parameters for NO2 with the C2v, Cs and Dsn symmetries, such as equilibrium geometry structures and energies, are calculated by the ab initio （CBS-Q） method.

Regulating the Nuclear Reactor through Changes of the Fraction of Delayed Neutrons: Theoretical Probabilities

In recent years а significant number of both theoretical and experimental works devoted to the influence of external electromagnetic fields and ionization on the probability of beta decays have been published. The present work investigates the feasibility of using this physical effect as the main mechanism for controlling the reactor. In this paper a system of equations is written and studied that allows one to describe the work of a nuclear reactor in the case where the probability of beta decay and, therefore, the fraction of delayed neu-trons is a function of time. It is shown that in the case of a constant fraction of delayed neutrons, the pro-posed system of equations is identical to the known system. As can be seen from analysis of a solution of the new system of equations for the proposed method of reactor control, acceleration by instantaneous neutrons is impossible even theoretically.

Study of scalar particles through the Klein–Gordon equation under rainbow gravity effects in Bonnor–Melvin-Lambda space-time

In our investigation,we explore the quantum dynamics of charge-free scalar particles through the Klein–Gordon equation within the framework of rainbow gravity,considering the Bonnor–Melvin-Lambda(BML)space-time background.The BML solution is characterized by the magnetic field strength along the axis of the symmetry direction which is related to the cosmological constantΛand the topological parameterαof the geometry.The behavior of charge-free scalar particles described by the Klein–Gordon equation is investigated,utilizing two sets of rainbow functions:(i)f(χ)=■,h(χ)=1 and(ii)f(χ)=1,h(χ)=1+βХ/2.Here 0<(Х=■)≤1 with E representing the particle's energy,Ep is the Planck's energy,andβis the rainbow parameter.We obtain the approximate analytical solutions for the scalar particles and conduct a thorough analysis of the obtained results.Afterwards,we study the quantum dynamics of quantum oscillator fields within this BML space-time,employing the Klein–Gordon oscillator.Here also,we choose the same sets of rainbow functions and obtain the approximate eigenvalue solution for the oscillator fields.Notably,we demonstrate that the relativistic approximate energy profiles of charge-free scalar particles and oscillator fields get influenced by the topology of the geometry and the cosmological constant.Furthermore,we show that the energy profiles of scalar particles receive modifications from the rainbow parameter and the quantum oscillator fields by both the rainbow parameter and the frequency of oscillation.

Reconstructing coherent dynamics of bound states induced by strong attosecond XUV pulses

We propose a scheme that utilizes weak-field-induced quantum beats to investigate the electronic coherences of atoms driven by a strong attosecond extreme ultraviolet(XUV)pulse.The technique involves using a strong XUV pump pulse to excite and ionize atoms and a time-delayed weak short pulse to probe the photoelectron signal.Our theoretical analysis demonstrates that the information regarding the bound states,initiated by the strong pump pulse,can be precisely reconstructed from the weak-field-induced quantum beat spectrum.To examine this scheme,we apply it to the attosecond XUV laser-induced ionization of hydrogen atoms by solving a three-dimensional time-dependent Schr?dinger equation.This work provides an essential reference for reconstructing the ultrafast dynamics of bound states induced by strong XUV attosecond pulses.

Klein–Gordon oscillator with magnetic and quantum flux fields in non-trivial topological space-time

The relativistic quantum motions of the oscillator field(via the Klein–Gordon oscillator equation)under a uniform magnetic field in a topologically non-trivial space-time geometry are analyzed.We solve the Klein–Gordon oscillator equation using the Nikiforov-Uvarov method and obtain the energy profile and the wave function.We discuss the effects of the non-trivial topology and the magnetic field on the energy eigenvalues.We find that the energy eigenvalues depend on the quantum flux field that shows an analogue of the Aharonov–Bohm effect.Furthermore,we obtain the persistent currents,the magnetization,and the magnetic susceptibility at zero temperature in the quantum system defined in a state and show that these magnetic parameters are modified by various factors.

Topological effects on non-relativistic eigenvalue solutions under AB-flux field with pseudoharmonic- and Mie-type potentials

In this paper,we investigate the quantum dynamics of a non-relativistic particle confined by the Aharonov-Bohm quantum flux field with pseudoharmonic-type potential in the background of topological defect produced by a point-like global monopole.We solve the radial Schrödinger equation analytically and determine the exact eigenvalue solution of the quantum system.Afterwards,we consider a Mie-type potential in the quantum system and solve the radial equation analytically and obtain the eigenvalue solution.We analyze the effects of the topological defect and the quantum flux with these potentials on the energy eigenvalue and wave function of the nonrelativistic particles.In fact,it is shown that the energy levels and wave functions are influenced by the topological defect shifted the result compared to the flat space results.In addition,the quantum flux field also shifted the eigenvalue solutions and an analogue of the Aharonov-Bohm effect for bound-states is observed.Finally,we utilize these eigenvalue solutions to some known diatomic molecular potential models and presented the energy eigenvalue and wave function.

Bismuthene quantum dots integrated D-shaped fiber as saturable absorber for multi-type soliton fiber lasers

In the present work,the uniformly sized bismuthene quantum dots(BiQDs)with an average diameter of 26 nm were fabricated via the solvothermal approach.By transferring the BiQDs onto the plane of micro-machined D-shaped fiber(DSF),a new type of saturable absorber(SA)was successfully prepared.Based on the evanescent field effect of D-shaped fiber,the prepared SA exhibits excellent saturable absorption properties with the maximum modulation depth of 5.1%at around 1.5μm.To further investigate its potential applications in ultrafast photonics,we demonstrated passive mode-locking operation in the erbium-doped fiber laser(EDFL)with BiQDs/DSF-SA.The conventional soliton pulses with duration of 835 fs at the repetition rate of 9.23 MHz and dissipative soliton pulses with duration of 575 fs at the repetition rate of 7.83 MHz were generated successfully.In addition,stable bound state of solitons with the pulse duration of 1.04 ps and sub-pulse time interval of 15.9 ps were also obtained based on the conventional soliton state by adjusting the pump power and polarization state.Our work reveals the great potential and capacity of BiQDs/DSF-SA in soliton mode-locking operations and promotes the explorative investigation of bismuth-based optoelectronic devices.

Exploring the light-quark interaction

Two basic motivations for an upgraded JLab facility are the needs： to determine the essential nature of light-quark confinement and dynamical chiral symmetry breaking （DCSB）; and to understand nucleon structure and spectroscopy in terms of QCD＇s elementary degrees of freedom. During the next ten years a programme of experiment and theory will be conducted that can address these questions. We present a Dyson- Schwinger equation perspective on this effort with numerous illustrations, amongst them： an interpretation of string^breaking; a symmetry-preserving truncation for mesons; the nucleon＇s strangeness σ-term; and the neutron＇s charge distribution.

Inverse scattering transforms of the inhomogeneous fifth-order nonlinear Schrodinger equation with zero/nonzero boundary conditions

The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent's series for the first time.Then,by combining with the robust IST,the Riemann-Hilbert(RH)problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed.Furthermore,based on the resulting RH problem,some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation.Finally,some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.