A Study of the Behavioral Controllability for Superposed Kuznetsov-Ma Soliton of the （3＋1）-Dimensional Generalized Nonlinear Schrodinger Equation

Abstract The （3＋1 ）-dimensional variable-coetfficient nonlinear SchrSdinger equation with linear and parabolic traps is studied, and an exact Kuznetsov-Ma soliton solution in certain parameter conditions is derived. These precise expressions indicate that diffraction and chirp factors influence phase, center and widths, while the gain/loss parameter only affects peaks. By adjusting the relation between the maximum accumulated time Tm and the accumulated time To based on maximum amplitude of Kuznetsov Ma soliton, postpone, maintenance and restraint of superposed Kuznetsov-Ma solitons are investigated.     

Moving bright solitons in a pseudo-spin polarization Bose-Einstein condensate

We study the moving bright solitons in the weak attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schr ?dinger equation with the variational method and the imaginary time evolution method,two kinds of solitons(plane wave soliton and stripe solitons) are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low.     

Kuznetsov–Ma soliton and Akhmediev breather of higher-order nonlinear Schrdinger equation

In terms of Darboux transformation, we have exactly solved the higher-order nonlinear Schrdinger equation that describes the propagation of ultrashort optical pulses in optical fibers. We discuss the modulation instability(MI) process in detail and find that the higher-order term has no effect on the MI condition. Under different conditions, we obtain Kuznetsov–Ma soliton and Akhmediev breather solutions of higher-order nonlinear Schrdinger equation. The former describes the propagation of a bright pulse on a continuous wave background in the presence of higher-order effects and the soliton's peak position is shifted owing to the presence of a nonvanishing background, while the latter implies the modulation instability process that can be used in practice to produce a train of ultrashort optical soliton pulses.     

Temporal development of open-circuit bright photovoltaic solitons

This paper investigates the temporal behaviour of open-circuit bright photovoltaic spatial solitons by using numerical techniques. It shows that when the intensity ratio of the soliton, the ratio between the soliton peak intensity and the dark irradiance, is small, the quasi-steady-state soliton width decreases monotonically with the increase of τ-, where τ- is the parameter correlated with the time, that when the intensity ratio of the soliton is big, the quasi-steady-state soliton width decreases with the increase of τ- and then increases with τ, and that the formation time of the steady-state solitons is not correlated with the intensity ratio of the soliton. It finds that the local nonlinear effect increases with the photovoltaic field, which behaves as that the width of soliton beams is small and the self-focusing quasi-period is short. On the other hand, we also discuss that both the time and the temperature have an effect on the beam bending.     

Pulse shaping of bright–dark vector soliton pair

We simulate pulse shaping of bright–dark vector soliton pair in an optical fiber system. Through changing input pulse parameters(amplitude ratio, projection angle, time delay, and phase difference), different kinds of pulse shapes and spectra can be generated. For input bright–dark vector soliton pair with the same central wavelength, "2 + 1"-and "2 + 2"-type pseudo-high-order bright–dark vector soliton pairs are achieved. While for the case of different central wavelengths,bright–dark vector soliton pairs with multiple pulse peaks/dips are demonstrated with appropriate pulse parameter setting.     

Soliton–cnoidal interactional wave solutions for the reduced Maxwell–Bloch equations

In this paper, we study soliton–cnoidal wave solutions for the reduced Maxwell–Bloch equations. The truncated Painlev′e analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell–Bloch equations with solitary wave, cnoidal periodic wave, and soliton–cnoidal interactional wave solutions in an explicit form.Particularly, the soliton–cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell–Bloch equations. Finally, we present some figures to show properties of the explicit soliton–cnoidal interactional wave solutions as well as some new dynamical phenomena.     

Exact Solutions to (3+1) Conformable Time Fractional Jimbo–Miwa,Zakharov–Kuznetsov and Modified Zakharov–Kuznetsov Equations

Exact solutions to conformable time fractional (3+1)-dimensional equations are derived by using the modified form of the Kudryashov method. The compatible wave transformation reduces the equations to an ODE with integer orders. The predicted solution of the finite series of a rational exponential function is substituted into this ODE.The resultant polynomial equation is solved by using algebraic operations. The method works for the Jimbo–Miwa, the Zakharov–Kuznetsov, and the modified Zakharov–Kuznetsov equations in conformable time fractional forms. All the solutions are expressed in explicit forms.     

Damped Kadomtsev–Petviashvili Equation for Weakly Dissipative Solitons in Dense Relativistic Degenerate Plasmas

We have investigated the properties of three-dimensional electrostatic ion solitary structures in highly dense collisional plasma composed of ultra-relativistically degenerate electrons and non-relativistic degenerate ions. In the limit of low ion-neutral collision rate, we have derived a damped Kadomtsev–Petviashvili(KP) equation using perturbation analysis. Supplemented by vanishing boundary conditions, the time varying solution of damped KP equation leads to a weakly dissipative compressive soliton. The real frequency behavior and linear damping of solitary pulse due to ion-neutral collisions is discussed. In the presence of weak transverse perturbations, soliton evolution with damping parameter and plasma density is delineated pointing out the extent of propagation using typical parameters of dense plasma in the interior of white dwarfs.     

Efect of Varying Dzyaloshinskii–Moriya Interaction on the Bistable Nano-Scale Soliton Switching

The efect of Dzyaloshinskii–Moriya(D-M) interaction on the bistable nano-scale soliton switching ofers the possiblity of developing a new innovative approach for data storage technology. The dynamics of Heisenberg ferromagnetic spin system is expressed in terms of generalized inhomogeneous higher order nonlinear Schro¨dinger(NLS) equation. The bistable soliton switching in the ferromagnetic medium is established by solving the associated coupled evolution equations for amplitude and velocity of the soliton using the fourth order Runge–Kutta method numerically.     

Stabilised bright solitons in Bose-Einstein condensates in an expulsive parabolic and complex potential

The exact solitonic solutions of the one-dimensional nonlinear Schr?dinger equation, which describes the dynamics of bright soliton in Bose—Einstein condensates with the time-dependent interaction in an expulsive parabolic and complex potential, are obtained by Darboux transformation. The results show that one can compress a bright soliton into an assumed peak of matter wave density by adusting the experimental parameter of the ratio of axial oscillation to radial oscillation or feeding parameter. Especially,when parameters satisfy the relation λ=2γ, the soliton is stable with time evolution without changing its shape and amplitude.     

Fundamental and dressed annular solitons in saturable nonlinearity with parity–time symmetric Bessel potential

We theoretically study the existence and stability of optical solitons in saturable nonlinearity with a two-dimensional parity–time(PT) symmetric Bessel potential.Besides the fundamental solitons,a novel type of dressed soliton,whose intensity looks like a ring dressed on an intensity hump,are presented.It is found that both the fundamental solitons and dressed solitons can exist when the propagation constant is beyond a certain critical value.The propagation stability is investigated with a linear stability analysis corroborated by a beam propagation method.All the fundamental solitons are stable,while dressed solitons are unstable for low values of saturable parameter.As the value of saturable parameter increases,the dressed solitons tend to be stable at high powers.     

PARTICULAR SOLITONS IN NONLINEAR LATTICE

One soliton of particle velocity and its amplitude (maximum particle velocity of one soliton) in Toda lattice is given analytically. It has also been known numerically that the maximum particle velocity (when the collision of two solitons reaches their maximum, we define V_n at this time as its maximum particle velocity) during the collision of two solitons moving in the same direction is equal to the difference between the amplitudes of two solitons if the difference is large enough; however, the maximum particle velocity is equal to the adding up of the amplitudes of two solitons moving in the opposite directions. The relationship between the maximum value of e^-(r_n)-1 and their initial amplitude of e^-(r_n)-1 is also given analytically in Toda lattice if the amplitudes of the two solitons are the same and their moving directions are opposite. Compared with the Boussinesq equation, there are differences between the Toda lattice equation and the Boussinesq equation for solitons during the collision.     

A multicomponent multiphase lattice Boltzmann model with large liquid–gas density ratios for simulations of wetting phenomena

A multicomponent multiphase(MCMP) pseudopotential lattice Boltzmann(LB) model with large liquid–gas density ratios is proposed for simulating the wetting phenomena. In the proposed model, two layers of neighboring nodes are adopted to calculate the fluid–fluid cohesion force with higher isotropy order. In addition, the different-time-step method is employed to calculate the processes of particle propagation and collision for the two fluid components with a large pseudoparticle mass contrast. It is found that the spurious current is remarkably reduced by employing the higher isotropy order calculation of the fluid–fluid cohesion force. The maximum spurious current appearing at the phase interfaces is evidently influenced by the magnitudes of fluid–fluid and fluid–solid interaction strengths, but weakly affected by the time step ratio.The density ratio analyses show that the liquid–gas density ratio is dependent on both the fluid–fluid interaction strength and the time step ratio. For the liquid–gas flow simulations without solid phase, the maximum liquid–gas density ratio achieved by the present model is higher than 1000:1. However, the obtainable maximum liquid–gas density ratio in the solid–liquid–gas system is lower. Wetting phenomena of droplets contacting smooth/rough solid surfaces and the dynamic process of liquid movement in a capillary tube are simulated to validate the proposed model in different solid–liquid–gas coexisting systems. It is shown that the simulated intrinsic contact angles of droplets on smooth surfaces are in good agreement with those predicted by the constructed LB formula that is related to Young's equation. The apparent contact angles of droplets on rough surfaces compare reasonably well with the predictions of Cassie's law. For the simulation of liquid movement in a capillary tube, the linear relation between the liquid–gas interface position and simulation time is observed, which is identical to the analytical prediction. The simulation results regarding the wetting phenomena of droplets on smooth/rough surfaces and the dynamic process of liquid movement in the capillary tube demonstrate the quantitative capability of the proposed model.     

Study of the optimal duty cycle and pumping rate for square-wave amplitude-modulated Bell–Bloom magnetometers

We theoretically and experimentally study the optimal duty cycle and pumping rate for square-wave amplitudemodulated Bell–Bloom magnetometers.The theoretical and the experimental results are in good agreement for duty cycles and corresponding pumping rates ranging over 2 orders of magnitude.Our study gives the maximum field response as a function of duty cycle and pumping rate.Especially,for a fixed duty cycle,the maximum field response is obtained when the time averaged pumping rate,which is the product of pumping rate and duty cycle,is equal to the transverse relaxation rate in the dark.By using a combination of small duty cycle and large pumping rate,one can increase the maximum field response by up to a factor of 2 or π /2,relative to that of the sinusoidal modulation or the 50% duty cycle square-wave modulation respectively.We further show that the same pumping condition is also practically optimal for the sensitivity due to the fact that the signal at resonance is insensitive to the fluctuations of pumping rate and duty cycle.     

Numerical approach for the evolution of spin-boson systems and its application to the Buck–Sukumar model

We study the evolution properties of spin-boson systems by a systematic numerical iteration approach, which performs well in the whole coupling regime. This approach evaluates a set of coefficients in the formal expression of the time-dependent Schr?dinger equation by expanding the initial state in Fock space. This set of coefficients is unique for the spin-boson Hamiltonian studied, allowing one to calculate the time evolution from different initial states. To complement our numerical calculations, we apply the method to the Buck–Sukumar model. We find that when the ground-state energy of the model is unbounded and no ground state exists in a certain parameter space, the time evolution of the physical quantities is naturally unstable.     

Soliton and rogue wave solutions of two-component nonlinear Schr?dinger equation coupled to the Boussinesq equation

The nonlinear Schr?dinger(NLS) equation and Boussinesq equation are two very important integrable equations.They have widely physical applications. In this paper, we investigate a nonlinear system, which is the two-component NLS equation coupled to the Boussinesq equation. We obtain the bright–bright, bright–dark, and dark–dark soliton solutions to the nonlinear system. We discuss the collision between two solitons. We observe that the collision of bright–bright soliton is inelastic and two solitons oscillating periodically can happen in the two parallel-traveling bright–bright or bright–dark soliton solution. The general breather and rogue wave solutions are also given. Our results show again that there are more abundant dynamical properties for multi-component nonlinear systems.     

Bouncing scenario of general relativistic hydrodynamics in extended gravity

In this paper,we have framed bouncing cosmological model of the Universe in the presence of general relativistic hydrodynamics in an extended theory of gravity.The metric assumed here is the flat Friedmann–Robertson–Walker space–time and the stress energy tensor is of perfect fluid.Since general relativity(GR)has certain issues with late time cosmic speed up phenomena,here we have introduced an additional matter geometry coupling that described the extended gravity to GR.The dynamical parameters are derived and analyzed.The dynamical behavior of the equation of state parameter has been analyzed.We have observed that the bouncing behavior is mostly controlled by the coupling parameter.     

An Estimation for the Power-Law Distribution Parameter Based on Entropy

A new estimation based on the Shannon entropy for the power-law distribution parameter is presented, The maximum likelihood estimation （MLE） of the parameter is discussed and the relation between the MLE and the moment estimation of the parameter is given out. It is shown that the minimum Shannon entropy estimation is equivalent to the MLE giving the log expectation.     

New analytical exact solutions of time fractional KdV KZK equation by Kudryashov methods

In this paper, new exact solutions of the time fractional KdV–Khokhlov–Zabolotskaya–Kuznetsov(KdV–KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann–Liouville derivative is used to convert the nonlinear time fractional KdV–KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV–KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics.The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV–KZK equation.     

Optimization of a magneto–optic trap using nanofibers

We experimentally demonstrate a reliable method based on a nanofiber to optimize the number of cold atoms in a magneto–optical trap(MOT) and to monitor the MOT in real time.The atomic fluorescence is collected by a nanofiber with subwavelength diameter of about 400 nm.The MOT parameters are experimentally adjusted in order to match the maximum number of cold atoms provided by the fluorescence collected by the nanofiber.The maximum number of cold atoms is obtained when the intensities of the cooling and re-pumping beams are about 23.5 mW/cm~2 and 7.1 mW/cm~2,respectively; the detuning of the cooling beam is-13.0 MHz, and the axial magnetic gradient is about 9.7 Gauss/cm.We observe a maximum photon counting rate of nearly(4.5 ± 0.1) × 10~5 counts/s.The nanofiber–atom system can provide a powerful and flexible tool for sensitive atom detection and for monitoring atom–matter coupling.It can be widely used from quantum optics to quantum precision measurement.