Dynamics of optical solitons,multipliers and conservation laws to the nonlinear schrödinger equation in (2+1)-dimensions with non-Kerr law nonlinearity

This work studies the (2 + 1)-dimensional nonlinear Schrödinger equation which arises in optical fibre. Grey and black optical solitons of the model are reported using a suitable complex envelope ansatz solution. The integration lead to some certain conditions which must be satisfied for the solitons to exist. On applying the Chupin Liu's theorem to the grey and black optical solitons, we construct new sets of combined optical soliton solutions of the model. Moreover, classification of conservation laws (Cls) of the model is implemented using the multipliers approach. This is achieved by constructing a set of first-order multipliers of a system of nonlinear partial differential equations acquired by transforming the model into real and imaginary components are derived, which are subsequently used to construct the Cls.     

Bright,dark and dark-singular soliton solutions of nonlinear Schrödinger's equation with spatio-temporal dispersion

This article presents an analytical study of the propagation of solitons through optical fibres. We consider a nonlinear Schrödinger equation with spatio-temporal dispersion and quadratic–cubic nonlinearity. Jacobi elliptic functions are used as an ansatz to extract optical dark and bright solitons as well as Jacobi elliptic solutions. The extended direct algebraic method gives dark and dark-singular soliton solutions. The constraint conditions which guarantee the existence of soliton solutions are listed.     

Analytic study on bound solitons and soliton collisions for the coupled nonlinear Schrödinger equations

A type of mode-locked fiber laser, which can generate the bound solitons in the anomalous group-velocity dispersion regime, is suggested in this paper via symbolic computation. A transformation is given to convert the coupled nonlinear Schrödinger equations to a simpler form. Analytic two-, three- and N-soliton solutions for the coupled nonlinear Schrödinger equations are obtained. Based on those solutions, formation of the bound solitons is analyzed, and methods for the soliton control are presented. The soliton intensity and collision period can be controlled with the changes in the nonlinearity and group-velocity dispersion of optical fibers. The slight phase shift has a great influence on the bound states of solitons after the soliton collision. To support the results, numerical simulations of three-soliton propagation are performed. Finally, the modulational instability of bound solitons is analyzed.     

Resonant optical solitons with parabolic and dual-power laws by semi-inverse variational principle

This paper obtains bright optical soliton solutions from resonant nonlinear Schrödinger’s equation by the aid of semi-inverse variational principle. The two forms of nonlinear media studied are parabolic and dual-power law. The necessary constraints for the existence of these solitons are also presented.     

Soliton collisions for a generalized variable-coefficient coupled Hirota–Maxwell–Bloch system for an erbium-doped optical fiber

In this paper, we construct soliton solutions for a generalized variable-coefficient coupled Hirota–Maxwell–Bloch system, which can describe the ultrashort optical pulse propagation in a nonlinear, dispersive fiber doped with two-level resonant atoms. Under certain transformations and constraints, one- and two-soliton solutions are obtained via the Hirota method and symbolic computation, and soliton collisions are graphically presented and analyzed. One soliton is shown to maintain its amplitude and shape during the propagation. Soliton collision is elastic, while bright two-peak solitons and dark two-peak solitons are also observed. We discuss the influence of the coefficients for the group velocity, group-velocity dispersion (GVD), self-phase modulation, distribution of the dopant, and Stark shift on the soliton propagation and collision features, with those coefficients are set as some constants and functions, respectively. We find the group velocity and self-phase modulation can change the solitons’ amplitudes and widths, and the solitons become curved when the GVD and distribution of the dopant are chosen as some functions. When the Stark shift is chosen as a certain constant, the two peaks of bright two-peak solitons and dark two-peak solitons are not parallel. In addition, we observe the periodic collision of the two solitons.     

光孤子通信系统的研究

光孤子（或超短光脉冲）的获得为光纤通信提供了一种非常高的速度。但是，光孤子之间的非线性作用大大限制了其通讯速度。在本文中，分析了光孤子相互作用对光通讯的影响，并提出了利用光放大及光压缩技术来消除损耗和光子间非线性作用的方案，该方法不仅能提高光通讯的比特率，且能够加大其通讯的距离。通常，在通讯距离给定的情况下，通讯系统的比特率可提高４０％以上。     

Bright and dark solitons in the normal dispersion regime of inhomogeneous optical fibers

In this letter, under investigation is a nonlinear Schrödinger equation with varying dispersion, nonlinearity and loss for the propagation of ultra-short optical pulses in the normal dispersion regime of optical fibers. By virtue of the modified Hirota's method and symbolic computation, the analytic two-soliton solution is explicitly obtained. Both the bright and dark solitons are observed in the normal dispersion regime of optical fibers with dispersion management. An asymptotic analysis to verify the elastic collision between solitons is performed and the stability of the soliton solutions is investigated. Besides, a new bright solitonic generator for generating high-power and narrow bandwidth pulses is advised. Furthermore, possible applicable soliton control techniques which might be used for the design of optical switch and dispersion-managed systems are proposed.     

Enigmas of optical and matter-wave soliton nonlinear tunneling

The method of mathematical analogies opens the possibility to study optical and matter-wave solitons in parallel and, due to the evident complexity of experiments with matter wave solitons, offers remarkable possibilities in studies of the BEC systems by performing experiments in the nonlinear optical systems and vice versa. We discuss previous misinterpretations of the binding soliton energy and investigate all possible scenarios of nonlinear soliton tunneling of Schrödinger solitons including soliton splitting on a potential barrier, leading to partial reflection and partial transmission, sub-barrier soliton tunneling and over-barrier soliton reflection. We reveal the most significant modifications of soliton tunneling scenarios due to increasing the binding energy, and show that the self-compressing soliton resembles more the classical particle case than a quantum mechanical behavior. The enhancement of the soliton binding energy is of decisive importance in the testing of a long-standing theoretical result which predicts that an optical soliton can tunnel between two regions of anomalous dispersion across a forbidden region of normal dispersion (enhanced soliton spectral tunneling effect).     

Symbolic computation on soliton dynamics and Bäcklund transformation for the generalized coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity

In this paper, we study the generalized coupled nonlinear Schrödinger equations with the cubic-quintic nonlinearity and arbitrary coupling parameters which describe the effects of the quintic nonlinearity on the ultrashort optical soliton pulse propagation in the non-Kerr media. Dark–dark N- and bright–dark two-soliton solutions are derived with symbolic computation. The bilinear Bäcklund transformation and the corresponding one-soliton solution are also given. Interactions of the dark–dark solitons including the repulsive and coherent interactions are investigated analytically and graphically, which are different from those in previous studies. The relationship between the amplitude and the velocity of the dark soliton is studied, especially the soliton with the small amplitude catches up with the one with the large amplitude. Head-on and overtaking interactions of dark–dark solitons are presented. Interactions between a stationary dark soliton and another dark one are shown. The asymptotic analysis shows that the interaction of dark–dark two solitons is elastic. The periodic attraction and repulsion of the bright–dark two solitons in the bound state are also analyzed, which are in accordance with those in the bright–dark vector soliton studies but different from the asymmetric and symmetric stationary bound states of Manakov bright–dark solitons.     

Mixed-type solitons for the coupled higher-order nonlinear Schrödinger equations in multi-mode and birefringent fibers

Abstract

In this paper, coupled higher-order nonlinear Schrödinger equations are studied for the ultrashort pulse propagation in such optical media as the multi-mode fibers and birefringent fibers. Through the Hirota method and symbolic computation, analytic mixed-type one- and two-soliton solutions are derived, and three sets of conditions for the non-singular solutions are given as well. Via the one-soliton solutions obtained, critical condition for the black and gray solitons is obtained analytically. Asymptotic analysis is carried out on the two-soliton solutions to derive the condition for the inelastic interaction. Evolution of the bound vector solitons, elastic and inelastic interactions between the two vector solitons are also investigated graphically. Moreover, after the inelastic interaction, the two bright solitons are observed to disappear, while the two dark ones form the new bound soliton.     

正常色散光纤消啁啾的孤子传输实验

利用正常色散光纤消啁啾成功地进行了１Ｇｂｉｔ／ｓ，２３公里的光弧子传输，观察到了一阶和高阶孤子传输现象，通过实验发现：采用适当长度的正常色散光纤消负啁啾，不仅能够压窄负啁啾的脉宽而且能够压窄频谱。     

Phase jitter control of ultrashort soliton in high-speed communication systems with nonlinear gain

An expression is derived for soliton phase jitter in soliton transmission with higher-order effects in the presence of nonlinear gain and filters. It is demonstrated that soliton phase jitter can be suppressed efficiently by nonlinear gain in addition to filters not only for long duration solitons but also for ultrashort solitons provided that the nonlinear gain coefficients satisfy specific conditions. This scheme offers an alternative means for the development of ultralong distance soliton transmission systems using differential phase-shift keying (DPSK), and exploits a robust technique to achieve a higher-speed soliton communication system using DPSK.     

Bright,dark, and singular solitons in optical fibers with spatio-temporal dispersion and spatially dependent coefficients

Abstract

Investigated in this work is the nonlinear Schrödinger equation with space-dependent parameters, which models the propagation of optical solitons in spatially inhomogeneous optical fiber with detuning, spatiotemporal dispersion, intermodal dispersion, and fiber gain or loss. Through the ansatz scheme, analytical bell, kink, and singular soliton solutions under certain coefficient constraints are obtained.     

Stochastic dark solitons for a higher-order nonlinear Schrödinger equation in the optical fiber

In this paper, a stochastic higher-order nonlinear Schrödinger equation, which describes the wave propagation in the optical fiber with stochastic dispersion and nonlinearity, is investigated analytically. Via the symbolic computation and white noise functional approach, the stochastic dark one- and two-soliton solutions are obtained, and effects of the Gaussian white noise on the stochastic dark one and two solitons are discussed. For the stochastic dark one soliton, velocity and phase change randomly because of the Gaussian white noise, but the energy, shape and amplitude keep unchanged during the soliton propagation. For the stochastic dark two solitons, effect of the Gaussian white noise leads to the inversion of the velocity directions, while the velocities have the same varying trend so that the interaction appears that the stochastic dark two solitons keep parallel.     

光纤中光孤子传输演化及相互作用研究

基于非线性薛定谔方程,采用分步傅立叶方法模拟了基阶、二阶和三阶皮秒光孤子以及光孤子对在光纤中的传输演化.结果表明,在长距离传输过程中基阶孤子的幅度和脉宽基本不变,是进行光孤子通信的理想载体.高阶孤子的幅度和脉宽变化较大,并呈现一种周期性的变化;孤子对的传输与两个脉冲的初始相位和输入强度相关.考虑三阶色散的飞秒量级孤子在光纤中的传输将不再出现对称性和周期性,脉冲的中心位置将发生偏移,同时脉冲的波形也会发生扭曲.     

Periodic waves and solitons in a nonlinear fibre with resonant impurities

We shall consider a coupled nonlinear Schrödinger equation-Bloch system of equations describing the propagation of a single pulse through a nonlinear dispersive waveguide in the presence of resonances; this could be, for example, a doped optical fibre. By making use of the integrability of the dynamic equations, we shall apply the finite-gap integration method to obtain periodic solutions for this system. Next, we consider the problem of the formation of solitons at a sharp front pulse and, by means of the Whitham modulational theory, we derive the amplitude and velocity of the largest soliton.     

Special foundation lecture: A personal view

Abstract

I (try to) review some of my work in theoretical quantum optics done over some 45 years. Highlights include discovery of ?optical solitons‘ as solutions to the nonlinear Maxwell-Bloch (MB) systems of equations as reported at the 1st National QE Conference, also at Owens Park, Manchester, in 1973. Bose-Einstein condensation (BEC) in magnetic traps at temperatures T ～ 10^?9K achieved in 1995 is described by forms of the quantum nonlinear Schrödinger (NLS) equation closely related to the quantized MB equations. It may be possible to see quantum soliton solutions of the quantum attractive NLS equation in one-dimensional (d = 1) magnetic traps holding the Bose condensed metal vapour ⁷Li. More generally such d = 1 quantum solitons may be significant to modern long-distance optical fibre communication, and perhaps to ?quantum information‘.     

Analytic study on soliton-effect pulse compression in dispersion-shifted fibers with symbolic computation

The soliton-effect pulse compression of ultrashort solitons in a dispersion-shifted fiber (DSF) is investigated based on solving the higher-order nonlinear Schrödinger equation with the effects of third-order dispersion (TOD), self-steepening (SS) and stimulated Raman scattering (SRS). By using Hirota's bilinear method with a set of parametric conditions, the analytic one-, two- and three-soliton solutions of this model are obtained. According to those solutions, the higher-order soliton is shown to be compressed in the DSF for the pulse with width in the range of a few picoseconds or less. An appealing feature of the soliton-effect pulse compression is that, in contrast to the second-order soliton compression due to the combined effects of negative TOD and SRS, the third-order soliton can significantly enhance the soliton compression in the DSF with small values of the group-velocity dispersion (GVD) at the operating wavelength.     

Vector single- and double-hump solitons for the coupled Sasa-Satsuma equations in optical media

In this paper, we investigate the coupled Sasa–Satsuma equations for the propagation of the ultrashort pulse in optical media. Through the binary Bell polynomials and introduction of three auxiliary functions, bilinear form, vector single- and double-hump soliton solutions in bright-dark form are obtained. To our knowledge, vector double-hump solitons in bright-dark form have not been studied in the existing literature. Based on those solutions, (i) parametric conditions for the existence of the vector single- and double-hump solitons, (ii) four types of soliton amplitudes and (iii) the interval between the two peaks for the double-hump soliton are presented analytically.     

Dark solitons for a discrete variable-coefficient Ablowitz–Ladik equation for an electrical/optical system

Under investigation in this paper is a discrete variable-coefficient Ablowitz–Ladik equation, which has certain applications in the electrical and optical systems. Employing the Hirota method and symbolic computation, we obtain the dark one- and two-soliton solutions under a variable-coefficient constraint. Linear-, parabolic-, periodic- and s-shaped dark one solitons are observed: We find that the space-time-modulated inhomogeneous frequency shift only affects the velocity of the dark soliton, the coefficient of tunnel coupling between the sites only affects the amplitude of the dark soliton, the time-modulated effective gain/loss term has no effect on either the dark soliton’s velocity or amplitude, and the velocity of the dark soliton decreases as the lattice spacing increases with the amplitude unchanged. Via the asymptotic analysis, we prove that the interactions between the dark two solitons are elastic on the soliton solutions. Overtaking interactions between the linear- and parabolic-shaped dark two solitons, as well as parallel linear- and s-shaped dark two solitons are plotted.