Effect of a barrier potential on soliton dynamical characteristics in condensates

By using the multiple-scale method, this paper analytically studies the effect of a barrier potential on the dynamical characteristics of the soliton in Bose--Einstein condensates. It is shown that a stable soliton is exhibited at the top of the barrier potential and the region of the absence of the barrier potential. Meanwhile, it is found that the height of the barrier potential has an important effect on the dark soliton dynamical characteristics in the condensates. With the increase of height of the barrier potential, the amplitude of the dark soliton becomes smaller, its width is narrower, and the soliton propagates more slowly.     

Control of soliton characteristics of the condensate by an arbitrary x-dependent external potential

This paper presents a family of soliton solutions of the one-dimensional nonlinear Schrdinger equation which describes the dynamics of the dark solitons in Bose-Einstein condensates with an arbitrary x-dependent external potential.The obtained results show that the external potential has an important effect on the dark soliton dynamical characteristics of the condensates.The amplitude,width,and velocity of the output soliton are relative to the source position of the external potential.The smaller the amplitude of the soliton is,the narrower its width is,and the slower the soliton propagates.The collision of two dark solitons is nearly elastic.     

Two-dimensional dark soliton in the nonlinear Schrödinger equation

Two-dimensional gray solitons to the nonlinear Schrödinger equation are numerically created by two processes to show its robustness. One is transverse instability of a one-dimensional gray soliton, and another is a pair annihilation of a vortex and an antivortex. The two-dimensional dark solitons are anisotropic and propagate in a certain direction. The two-dimensional dark soliton is stable against the head-on collision. The effective mass of the two-dimensional dark soliton is evaluated from the motion in a harmonic potential.     

Matter-wave solitons in the presence of collisional inhomogeneities: Perturbation theory and the impact of derivative terms

We study the dynamics of bright and dark matter-wave solitons in the presence of a spatially varying nonlinearity. When the spatial variation does not involve zero crossings, a transformation is used to bring the problem to a standard nonlinear Schrödinger form, but with two additional terms: an effective potential one and a non-potential term. We illustrate how to apply perturbation theory of dark and bright solitons to the transformed equations. We develop the general case, but primarily focus on the non-standard special case whereby the potential term vanishes, for an inverse square spatial dependence of the nonlinearity. In both cases of repulsive and attractive interactions, appropriate versions of the soliton perturbation theory are shown to accurately describe the soliton dynamics.     

Soliton dynamical properties of Boseben Einstein condensates trapped in a double square well potential

We first present an analytical solution of the single and double solitions of Bose-Einstein condensates trapped in a double square well potential using the multiple-scale method. Then, we show by numerical calculation that a dark soliton can be transmitted through the square well potential. With increasing depth of the square well potential, the amplitude of the dark soliton becomes larger, and the soliton propagates faster. In particular, we treat the collision behaviour of the condensates trapped in either equal or different depths of the double square well potential. If we regard the double square well potential as the output source of the solitons, the collision locations (position and time) between two dark solitons can be controlled by its depth.     

Separate spatial holographic and two-photon-Hamiltonian soliton pairs in an unbiased series photorefractive crystal circuit

This paper presents calculations for an idea in photorefractive spatial solitons, namely, a dissipative holographic soliton and a two-photon-Hamiltonian spatial soliton in one dimension form in an unbiased series photorefractive crystal circuit consisting of a single-photon photorefractive crystals and a two-photon one of which at least one must be photovoltaic. The two solitons are known collectively as a separate Holographic–Hamiltonian spatial soliton pair and there are two types: dark–dark and bright–dark if only one crystal of circuit is photovoltaic. The results show that the two-photon-Hamiltonian soliton in a soliton pair can affect the holographic one by light-induced current and the holographic soliton cannot affect the two-photon-Hamiltonian one.     

Propagation characteristics of parallel dark solitons in silicon-on-insulator waveguide

The propagation characteristic of two identical and parallel dark solitons in a silicon-on-insulator(SOI) waveguide is simulated numerically using the split-step Fourier method. The parallel dark solitons imposed by the initial chirp are investigated mainly by changing their power, their relative time delay. The simulation shows that the time delay deforms the parallel dark soliton pulse, forming a bright-like soliton in the transmission process and making the transmission quality down. By increasing the power of one dark soliton, the energy of the other dark soliton can be increased, and larger increase in a soliton's power leads to larger increase in the energy of the other. When the initial chirp is introduced into one of the dark solitons, higher energy consumption is observed. In particular, positive chirps resulting in pulse broadening width while negative chirps narrowing, with an obvious compression effect on the other dark soliton. Finally, large negative chirps are found to have a profound impact on parallel and nonparallel dark solitons.     

Multi-Solitons and Combined Solitons with Self-Similar Behaviors in a Birefringent Fiber with Higher-Order Effects

A coupled variable-coefficient higher-order nonlinear Schr(o|¨)dinger equation in biretringent fiber is studied,and analytical multi-soliton,combined bright and dark soliton,W-shaped and M-shaped soliton solutions are obtained.Nonlinear tunnelling of these combined solitons in dispersion barrier and dispersion well on an exponential background is discussed,and the decaying or increasing,even lossless tunnelling behaviors of combined solitons are decided by the decaying or increasing parameter.     

Dynamics of Spatial Dark Solitons Trapped in the Media with Gain and TPA

The propagation of dark solitons in nonlinear media that include gain and Joss described by a nonlinear Schroedinger equation is investigated. Based on the direct approach of perturbation theorv, the width, height and other related quantities of dark solitons are obtained. It is shown that stationarv propagation of dark solitons is found to be possible in the presence of both gain and absorption. The results obtained by means of our analytic method are in excellent agreement with numerical simulations. Our results are helpful for the research into the optical soliton transmission system.     

Dark soliton in the Bose-Einstein condensates with nonlinearity and harmonic potential managements

The dynamics of dark solitons in one-dimensional Bose-Einstein condensates under the nonlinearity and harmonic potential managements is investigated. It is found that at the large particle limit the macroscopic wave function could evolve self-similarly, which provides a time-varying background for the propagation of dark solitons. The approximate dark soliton solution is derived and its center-of-mass motion is predicted analytically.     

Dissipative solitons of the Bose-Einstein condensate of excitons

A mirrorless scheme for forming dissipative solitons has been proposed. It consists of a thin layer of a nonlinear medium excited by coherent laser radiation. The existence of dark dissipative solitons of the Bose-Einstein condensate of excitons in such a semiconductor film has been numerically demonstrated. The sizes of an excition soliton and required laser-radiation level are two orders of magnitude smaller than the respective quantities for the case of optical dissipative solitons.     

Feshbach resonance management of vector solitons in two-component Bose—Einstein condensates

We consider two coupled Gross-Pitaevskii equations describing a two-component Bose-Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential,and investigate the dynamics of vector solitons.By using a direct method,we construct a novel family of vector soliton solutions,which are the linear combination between dark and bright solitons in each component.Our results show that due to the superposition between dark and bright solitons,such vector solitons possess many novel and interesting properties.The dynamics of vector solitons can be controlled by the Feshbach resonance technique,and the vector solitons can keep the dynamic stability against the variation of the scattering length.     

Formation of multiple dark photovoltaic spatial solitons

We theoretically study the formation of multiple dark photovoltaic soliton splitting in the quasi-steady-state and steady-state regimes under open-circuit conditions. We find that the initial width of the dark notch at the entrance face of the crystal is a key parameter for generating an even (or odd) number sequence of dark coherent photovoltaic solitons. If the initial width of the dark notch is small, only a fundamental soliton or Y-junction soliton pair is generated. As the initial width of the dark notch is increased, the dark notch tends to split into an odd (or even) number of multiple dark photovoltaic solitons, which realizes a progressive transition from a low-order soliton to a sequence of higher-order solitons. The soliton pairs far away from the centre have bigger width and less visibility. In addition, when the distance from the centre of the dark notch increases, the separations between adjacent dark stripes become slightly smaller.     

Dark and anti-dark vector solitons of the coupled modified nonlinear Schrödinger equations from the birefringent optical fibers

Coupled modified nonlinear Schr?dinger (CMNLS) equations describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. A new type of the Lax pair and another hierarchy of the infinitely many conservation laws are derived based on the Wadati-Konno-Ichikawa system. By means of the Hirota method, soliton solutions in the normal dispersion regime are obtained. Parametric regions for the existence of dark and anti-dark vector soliton solutions are given. Asymptotic analysis shows that the collision between two solitons (two anti-dark solitons, two dark solitons, or dark and anti-dark solitons) in each polarization direction is elastic. Moreover, there is no energy transfer between two polarization components of each vector soliton, whether dark or anti-dark vector soliton. In addition, dark and anti-dark solitons can coexist on the same background seen from the collision between the dark and anti-dark solitons in one polarization direction. Our graphical analysis shows that the parameters in the CMNLS equations not only determine the regions for the existence of dark and anti-dark soliton solutions but also control the phase and direction of the propagation of the solitons. Finally, through the linear stability analysis, the modulational instability condition is given.     

Oscillation properties of matter-wave bright solitons in harmonic potentials

We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter- and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton (without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects.     

Dynamics of Bright/Dark Solitons in Bose--Einstein Condensates with Time-Dependent Scattering Length and External Potential

We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton＇s parameters （amplitude, width, and period） can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.     

Matching group velocity of bright and/or dark solitons via double-dark resonances

We propose a scheme which can generate group velocity matching bright and/or dark solitons in a four-level tripod configuration atomic system via double-dark resonances. It is shown that the linear absorption properties can be controlled by the controlling fields. For the nonlinear case, the optical soliton can form in the first and second electromagnetically induced transparency windows and their group velocities can be matched under the condition of equal half Rabi frequencies of the two controlling fields. We also show that adjusting the amplitude and group velocity of the soliton as well as the bright and dark solitons conversion can be realized.     

Effects of periodic optical lattice potential on dark solitons in a Bose Einstein condensate

This paper investigates the dynamics of dark solitons in a Bose--Einstein condensate with a magnetic trap and an optical lattice (OL) trap, and analyses the effects of the periodic OL potential on the dynamics by applying the variational approach based on the renormalized integrals of motion. The results show that the dark soliton becomes only a standing-wave and free propagation of the dark soliton is not possible when the periodic length of the OL potential is approximately equal to the effective width of the dark soliton. When the periodic length is very small or very large, the effects of the OL potential on the dark soliton will be sharply reduced. Finally, the numerical results confirm these theoretical findings.     

Dark solitons in a two-component Bose-Einstein condensate

The creation and interaction of dark solitons in a two-component Bose-Einstein condensate is investigated. For a miscible case, the interaction of dark solitons in different components is studied. Various possible scenarios are presented, including the formation of a soliton-soliton bound pair. We also analyze the soliton propagation in the presence of domains, and show that a dark soliton can be transferred from one component to the other at the domain wall when it exceeds a critical velocity. For lower velocities multiple reflections within the domain are observed, where the soliton is evaporated and accelerated after each reflection until it finally escapes from the domain.     

非均匀光纤中暗孤子传输特性研究

由于变系数非线性Schrödinger方程的增益、色散和非线性项都是变化的, 根据方程这一特点可以研究光脉冲在非均匀光纤中的传输特性. 本文利用Hirota方法, 得到非线性Schrödinger方程的解析暗孤子解. 然后根据暗孤子解对暗孤子的传输特性进行讨论, 并且分析各个物理参量对暗孤子传输的影响. 经研究发现, 通过调节光纤的损耗、色散和非线性效应都能有效的控制暗孤子的传输, 从而提高非均匀光纤中的光脉冲传输质量. 此外, 本文还得到了所求解方程的解析双暗孤子解, 最后对两个暗孤子相互作用进行了探讨. 本文得到的结论有利于研究非均匀光纤中的孤子控制技术.