Dark soliton interaction in optical time division multiplexed system with randomly varying birefringence and random dispersion map

Correlated perturbations caused by both randomly varying birefringence and random dispersion map are considered in optical time division multiplexed dispersion-managed dark soliton system, and their effects on soliton interaction are investigated numerically. These perturbations enhance soliton interaction, and their effects relate to the strength of perturbation, separation, and pulse width. The correlation plays an important role ar d reinforces these effects. Moreover, there is a stochastic limit between two perturbations in the system, where the effect is the largest and the corresponding interaction distance is the shortest.     

Submergence and Control of Dark Soliton in a Dispersion—Managed System with Random Dispersion Map

Random dispersion map is considered in a dispersion-managed dark soliton system,its influence on soliton propagation and interaction is discussed.It is found that the random dispersion map results in large sidebands leads to submergence of dark soliton,and enhances the interaction between solitons.Finally,nonlinear gain is introduced to suppress the influence effectively.     

Correlation between randomly varying birefringence and random dispersion map in a dispersion-managed soliton system

The correlation between perturbations caused by randomly varying birefringence and a random dispersion map is considered in a dispersion-managed soliton system, and their effects on soliton propagation and interaction are investigated numerically. These perturbations lead to the disintegration of a soliton, and enhance the interaction between solitons. The correlation plays an important role, and reinforces these effects. Furthermore, there is a stochastic resonance between two perturbations in the system; here the effect is the largest, and the corresponding distance until disintegration is the shortest. Finally, nonlinear gain and a filter are introduced to effectively suppress these effects.     

Effects of correlated perturbations on dark soliton propagation and interaction

Correlated perturbations are considered in a dark soliton system, and their effects on soliton propagation and interaction are investigated numerically. These perturbations result in large sidebands, lead to submergence of dark soliton, and enhance the interaction. The correlation amplifies these effects and shortens the distance until submergence. The comparison of the distinction is made between the degradations of these effects on dark soliton and the corresponding bright soliton. It is found that these effects on dark soliton are less than those on bright soliton. Finally the nonlinear gain is introduced to suppress efficiently these effects.     

Dark soliton in one-dimensional Bose–Einstein condensate under a periodic perturbation of trap

The perturbation of a confining trap leads to the collective oscillation of a Bose--Einstein condensate, thereby the propagation of a dark soliton in the condensate is affected. In this study, periodic perturbation is employed to match the soliton oscillation. We find that the soliton dynamics depends sensitively on the coupling between the moving direction of the trap and that of the soliton. The soliton energy/depth evolves periodically, and a relevant shift in the soliton trajectory occurs as compared with the unperturbed case. Overall, the soliton oscillation frequency changes little even if the perturbation amplitude and frequency vary.     

Propagation of bright femtosecond pulses in a nonlinear optical fibre with the third- and fourth-order dispersions

We solve the generalized nonlinear Schr\"{o}dinger equation describing the propagation of femtosecond pulses in a nonlinear optical fibre with higher-order dispersions by using the direct approach to perturbation for bright solitons, and discuss the combined effects of the third- and fourth-order dispersions on velocity, temporal intensity distribution and peak intensity of femtosecond pulses. It is noticeable that the combined effects of the third- and fourth-order dispersions on an initial propagated soliton can partially compensate each other, which seems to be significant for the stability controlling of soliton propagation features.     

Influence of group—velocity mismatch on soliton switching in a nonlinear fibre coupler

In this work, the influence of group-velocity mismatch on soliton self-routing pulse switching in a nonlinear fibre coupler is discussed in detail by the use of both variational approach and numerical simulation. The results obtained show that the group-velocity mismatch leads to the relative displacement between the two orthogonal polarization modes, increase of the critical power, and reduction of the elimination-light ratio. For sub-ps pulse, the influence cannot be neglected.     

Propagation and interaction of ion-acoustic solitary waves in a quantum electron-positron-ion plasma

This paper discusses the existence of ion-acoustic solitary waves and their interaction in a dense quantum electron-positron-ion plasma by using the quantum hydrodynamic equations.The extended Poincar’e-Lighthill-Kuo perturbation method is used to derive the Korteweg-de Vries equations for quantum ion-acoustic solitary waves in this plasma.The effects of the ratio of positrons to ions unperturbation number density p and the quantum diffraction parameter H e (H p) on the newly formed wave during interaction,and the phase shift of the colliding solitary waves are studied.It is found that the interaction between two solitary waves fits linear superposition principle and these plasma parameters have significantly influence on the newly formed wave and phase shift of the colliding solitary waves.The investigations should be useful for understanding the propagation and interaction of ion-acoustic solitary waves in dense astrophysical plasmas (such as white dwarfs) as well as in intense laser-solid matter interaction experiments.     

On Time-Fractional Cylindrical Nonlinear Equation

Properties of cylindrical electron acoustic solitons are studied in vortex plasmas.The modified cylindrical Korteweg-de Vries(KdV) equation is acquired and converted into the time fractional cylindrical modified KdV equation by Agrawal's analysis.Via the Adomian decomposition method,a cylindrical soliton solution to the equation is obtained.The cylindrical time fractional effect on the wave properties is investigated.Further,the increase of the fractional order of time a and hot to trapped electrons temperature β are minimized in both solitary width and amplitude.These influences on the structures of the soliton may be an alternative to the use of higher order perturbation analysis.     

Influence of Spectral Filtering and Nonlinear Gain on an Optical Soliton

Using the direct soliton perturbation theory, we investigate the evolution of soliton parameters and the firstorder correction of bright soliton in a system with linear and nonlinear gain （or loss） and spectral filtering in a comprehensive way. The results obtained by means of our analytic method are consistent with numerical simulations. It is also found that the stable soliton propagation which has been investigated in a previous report by others is the limit case of our results.     

Dark soliton interaction in optical time division multiplexed system with randomly varying birefringence and random dispersion map

Correlated perturbations caused by both randomly varying birefringence and random dispersion map are considered in optical time division multiplexed dispersion-managed dark soliton system, and their effects on soliton interaction are investigated numerically. These perturbations enhance soliton interaction, and their effects relate to the strength of perturbation, separation, and pulse width. The correlation plays an important role and reinforces these effects. Moreover, there is a stochastic limit between two perturbations in the system, where the effect is the largest and the corresponding interaction distance is the shortest.     

Approxiamation theory for unequal amplitude soliton pairs in nonliear optical fibers

The equivalent-particle approach is used to investigate the interaction of two unequal-amplitude solitons propagating in nonlinear fibers by regarding the interaction as a perturbation. The Newtonian equations for the motion of solitons are given. Results show that the interaction of an unequal-amplitude soliton pair can be approximated as the product of a local interaction factor dependent on the propagation distance and a nonlocal interaction factor independent of the propagation distance. The local factor forces soliton interaction to alternate between the attractive and the repulsive, and, on a large scale, the average of this character markedly reduces the interaction of the unequal-amplitude solitons.     

随机色散对孤子传输系统时间抖动影响

在分布放大传输系统中建立了随机色散模型,利用自伴算符法研究了随机色散的影响。结果表明:随机色散与放大的自发辐射噪音联合作用增大了传输系统的时间抖动,其中与传输距离有关的随机色散具有长距离效应,而与孤子频移有关的随机色散具有短距离效应。     

APPROACH FOR THE STUDY OF SOLITON IN OPTICAL FIBER

In the anomalous group velocity dispersion regime, under the influence of optical Kerr nonlinearity, the monomode optical fiber supports stable propagation of an initial soliton pulse. In this paper, we present a singular perturbation approach for the study of various perturbations acting on this initial soliton pulse, In contrast with the previous perturbation theory for this subject, this approach gets rid of dependence on any tool of the sophisticated inverse scattering transform.     

Optical solitons in resonant and nonresonant nonlinear media in the presence of perturbations

We studied the optical solitons in nonlinear resonant and nonresonant media in the presence of perturbations, assuming that the transient effects are stimulated by the light scanning beam. We treated a slight deviation from the exact necessary condition for the soliton existence (2betanu=1), as a small perturbation for the integrable system, studying its influence upon the soliton propagation conditions. The approximation is constructed by the help of an algebraic version of the soliton perturbation theory using a Riemann boundary problem in connection with the inverse scattering method. We have obtained the soliton equation and we have solved it in the presence of a small perturbation in the adiabatic approximation. In this case we have demonstrated that for a Lorentz profile line the amplitude of the soliton remains unchanged, the only effect of the perturbation results in a phase shift.     

Dynamics of bound vector solitons induced by stochastic perturbations: Soliton breakup and soliton switching

We respectively investigate breakup and switching of the Manakov-typed bound vector solitons (BVSs) induced by two types of stochastic perturbations: the homogenous and nonhomogenous. Symmetry-recovering is discovered for the asymmetrical homogenous case, while soliton switching is found to relate with the perturbation amplitude and soliton coherence. Simulations show that soliton switching in the circularly-polarized light system is much weaker than that in the Manakov and linearly-polarized systems. In addition, the homogenous perturbations can enhance the soliton switching in both of the Manakov and non-integrable (linearly- and circularly-polarized) systems. Our results might be helpful in interpreting dynamics of the BVSs with stochastic noises in nonlinear optics or with stochastic quantum fluctuations in Bose–Einstein condensates.     

Bright and dark solitons in the normal dispersion regime of inhomogeneous optical fibers: Soliton interaction and soliton control

Symbolically investigated in this paper is a nonlinear Schrödinger equation with the varying dispersion and nonlinearity for the propagation of optical pulses in the normal dispersion regime of inhomogeneous optical fibers. With the aid of the Hirota method, analytic one- and two-soliton solutions are obtained. Relevant properties of physical and optical interest are illustrated. Different from the previous results, both the bright and dark solitons are hereby derived in the normal dispersion regime of the inhomogeneous optical fibers. Moreover, different dispersion profiles of the dispersion-decreasing fibers can be used to realize the soliton control. Finally, soliton interaction is discussed with the soliton control confirmed to have no influence on the interaction. The results might be of certain value for the study of the signal generator and soliton control.     

Dynamics of solitons in periodic systems with different nonlinear media

To analyze pulse dynamics in an optical system consisting of a periodic sequence of nonlinear media, a composite model is used. It includes a model of the resonance interaction of an ultrashort light pulse with the energy transition of the medium with allowance made for an upper level pump and an almost integrable model that describes the propagation of the light field in the other medium with a cubic nonlinearity and dispersion. Additional allowance is made for losses and other kinds of interaction by introducing perturbation terms. On the bases of the inverse scattering transform and perturbation theory, a simple method for analyzing specific features of soliton evolution in periodic systems of this kind is developed. It is used to describe various modes of soliton evolution in such a system, including chaotic dynamics.