In the present work, we numerically explore the existence and stability properties of different types of configurations of dark-bright solitons, dark-bright soliton pairs and pairs of dark-bright and dark solitons in discrete settings, starting from the anti-continuum limit. We find that while single discrete dark-bright solitons have similar stability properties to discrete dark solitons, their pairs may only be stable if the bright components are in phase and are always unstable if the bright components are out of phase. Pairs of dark-bright solitons with dark ones have similar stability properties as individual dark or dark-bright ones. Lastly, we consider collisions between dark-bright solitons and between a dark-bright one and a dark one. Especially in the latter and in the regime where the underlying lattice structure matters, we find a wide range of potential dynamical outcomes depending on the initial soliton speed.
We study the dynamics of two-component vector solitons, namely, bright-bright (BB) solitons interacting with parity-time-($\mathcal{PT}$) symmetric potentials. We employ direct numerical simulations to demonstrate the unidirectional segregation of the BB soliton. Using a modified perturbed dynamical variational Lagrangian approximation, we develop an analytical model to verify the results obtained from the numerical calculations. Simplified variational equations of motion suggest that the splitting of BB solitons can be explained by considering the effective force between the two components.
We study the topological phase of bright soliton with arbitrary velocity under the self-steepening effect. Such topological phase can be described by the topological vector potential and effective magnetic field. We find that the point-like magnetic fields corresponds to the density peak of such bright solitons, where each elementary magnetic flux is π. Remarkably, we show that two bright solitons can generate an additional topological field due to the phase jump between them. Our research provided the possibility to use bright solitons to explore topological properties.
We theoretically demonstrate a mechanism for bright soliton generation in spinor non-equilibrium Bose-Einstein condensates made of atoms or quasiparticles such as polaritons in semiconductor microcavities. We give analytical expressions for bright (half) solitons as minimizing functions of a generalized non-conservative Lagrangian elucidating the unique features of inter and intra-competition in non-equilibrium systems. The analytical results are supported by a detailed numerical analysis that further shows the rich soliton dynamics inferred by their instability and mutual cross-interactions.
In this paper, a generalized long-wave short-wave resonance interaction system, which describes the nonlinear interaction between a short-wave and a long-wave in fluid dynamics, plasma physics and nonlinear optics, is considered. Using the Hirota bilinear method, the general $N$-bright and $N$-dark soliton solutions are deduced and their Gram determinant forms are obtained. A special feature of the fundamental bright soliton solution is that, in general, it behaves like the Korteweg-deVries soliton. However, under a special condition, it also behaves akin to the nonlinear Schrödinger soliton w…
We study analytically and numerically envelope solitons (bright and gap solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schrödinger equation and obtain analytical expressions for bright and gap solitons. We also perform d…
Bright soliton interactions in the variable coefficient Fokas-Lenells equation, Conservation laws, Modulation instability and Soliton tunneling
Department of Physics, Cotton University（科顿大学物理系）；Department of Nonlinear Dynamics, Bharathidasan University（巴拉迪达桑大学非线性动力学系）；Department of Physics, Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校物理系）
In the present work, we explore the potential of spin-orbit (SO) coupled Bose-Einstein condensates to support multi-component solitonic states in the form of dark-bright (DB) solitons. In the case where Raman linear coupling between components is absent, we use a multiscale expansion method to reduce the model to the integrable Mel'nikov system. The soliton solutions of the latter allow us to reconstruct approximate traveling DB solitons for the reduced SO coupled system. For small values of the formal perturbation parameter, the resulting waveforms propagate undistorted, while for large value…
We consider the dynamics and stability of bright soliton stripes in the two-dimensional nonlinear Schrödinger equation with hyperbolic dispersion, under the action of transverse perturbations. We start by discussing a recently proposed adiabatic-invariant approximation for transverse instabilities and its limitations in the bright soliton case. We then focus on a variational approximation used to reduce the dynamics of the bright-soliton stripe to effective equations of motion for its transverse shift. The reduction allows us to address the stripe's snaking instability, which is inherently pre…
Solitons in general are configurations of extended fields which move like isolated particles. Vector bright solitons can occur in a two-component self-attractive Bose-Einstein condensate. If the components of the condensate have different chemical potentials, the total spin of the soliton can serve as an internal energy depot that makes the soliton into an \emph{active} particle, able to move against an external force using energy carried within the particle -- if there is a dynamical mechanism for steadily transferring energy from soliton spin into soliton motion. Here we present such a dynam…
The dynamics of non-autonomous bright matter-wave solitons in Rabi coupled binary Bose-Einstein condensates is explored. By performing a unitary and similarity/lens-type transformation, we reduce the non-autonomous Gross-Pitaevskii equation into the celebrated Manakov model. Then, we construct the exact bright solitons of the non-autonomous Gross-Pitaevskii system in the presence of time dependent nonlinearities for two specific forms, namely hyperbolic nonlinearities, which are of physical interest. The experimental possibilities of realizing the forms of temporally modulated potentials corre…
Under investigation in this paper are the coupled complex short pulse equations, which describe the propagation of ultra-short optical pulses in cubic nonlinear media.Through the Hirota method, bright-dark one- and two-soliton solutions are obtained. Interactions between two bright or two dark solitons are verified to be elastic through the asymptotic analysis. With different parameter conditions of the vector bright-dark two solitons, the oblique interactions, bound states of solitons and parallel solitons are analyzed.
我们证明了由于偶极排斥接触相互作用而在中心平面上形成的强、稳定、可移动的准一维暗中亮偶极玻色-爱因斯坦凝聚体（BEC）孤子.在中等速度下，两个这样的孤子碰撞的头被发现是几乎没有变形的准弹性。本文还讨论了在实验室中利用相位印记产生偶极明中暗孤子的方案。在偶极二元BEC中可以形成丰富多样的暗中亮孤子，可以是一个暗中亮孤子与一个亮孤子耦合，也可以是两个暗中亮孤子耦合。结果表明，使用数值模拟在三个空间维度采用现实的相互作用参数的偶极164 Dy BEC和二进制164 Dy-162 Dy BEC。
We study the statics and dynamics of anisotropic, stable, bright and dark-in-bright dipolar quasi-two-dimensional Bose-Einstein condensate (BEC) solitons on a one-dimensional (1D) optical-lattice (OL) potential. These solitons mobile in a plane perpendicular to the 1D OL trap can have both repulsive and attractive contact interactions. The dark-in-bright solitons are the excited states of the bright solitons. The solitons, when subject to a small perturbation, exhibit sustained breathing oscillation. The dark-in-bright solitons can be created by phase imprinting a bright soliton. At medium vel…
We demonstrate stable and metastable vortex-bright solitons in a three-dimensional spin-orbit-coupled three-component hyperfine spin-1 Bose-Einstein condensate (BEC) using numerical solution and variational approximation of a mean-field model. The spin-orbit coupling provides attraction to form vortex-bright solitons in both attractive and repulsive spinor BECs. The ground state of these vortex-bright solitons is axially symmetric for weak polar interaction. For a sufficiently strong ferromagnetic interaction, we observe the emergence of a fully asymmetric vortex-bright soliton as the ground s…
We report experimental observation of incoherently coupled dark-bright vector solitons in single-mode fibers. Properties of the vector solitons agree well with those predicted by the respective systems of incoherently coupled nonlinear Schroedinger equations. To the best of our knowledge, this is the first experimental observation of temporal incoherently coupled dark-bright solitons in single-mode fibers.
We show how access to sufficiently flexible trapping potentials could be exploited in the generation of three-dimensional atomic bright matter-wave solitons. Our proposal provides a route towards producing bright solitonic states with good fidelity, in contrast to, for example, a non-adiabatic sweeping of an applied magnetic field through a Feshbach resonance.
We derive exact analytical expressions for the spatial Fourier spectrum of the fundamental bright soliton solution for the $(1 + 1)$-dimensional nonlinear Schrödinger equation. Similar to a Gaussian profile, the Fourier transform for the hyperbolic secant shape is also shape-preserving. We further confirm that the fundamental soliton indeed satisfies essential characteristics such as Parseval's relation and the stretch-bandwidth reciprocity relationship. The fundamental bright solitons find rich applications in nonlinear fiber optics and optical telecommunication systems.
In this work we present a systematic theoretical analysis regarding dark-bright solitons and their interactions, motivated by recent advances in atomic two-component repulsively interacting Bose-Einstein condensates. In particular, we study analytically via a two-soliton ansatz adopted within a variational formulation the interaction between two dark-bright solitons in a homogeneous environment beyond the integrable regime, by considering general inter/intra-atomic interaction coefficients. We retrieve the possibility of a fixed point in the case where the bright solitons are out of phase. As …
We theoretically study bright and dark solitons in an experimentally relevant hybrid system characterized by strong light-matter coupling. We find that the corresponding two-component model supports a variety of coexisting moving solitons including bright solitons on zero and nonzero background, dark-gray and gray-gray dark solitons. The solutions are found in the analytical form by reducing the two-component problem to a single stationary equation with cubic-quintic nonlinearity. All found solutions coexist under the same set of the model parameters, but, in a properly defined linear limit, a…
We study collisions of moving nonlinear-Schrödinger solitons with a $\mathcal{PT}$-symmetric dipole embedded into the one-dimensional self-focusing or defocusing medium. Accurate analytical results are produced for bright solitons, and, in a more qualitative form, for dark ones. In the former case, an essential aspect of the approximation is that it must take into regard the intrinsic chirp of the soliton, thus going beyond the framework of the simplest quasi-particle description of the soliton's dynamics. Critical velocities separating reflection and transmission of the incident bright solito…
A vortex-bright soliton can precess around a fix point. Here, we find numerically that the fixed point and the associated precessional orbits can be shifted by applying a constant driving force on the bright component, the displacement is proportional to the force with a minus sign. This robust dynamics is then discussed theoretically by treating the vortex-bright soliton as an effective point particle, explaining the observed dynamics and predicting new ones that are subsequently confirmed. By appropriately tuning the force, the vortex-bright soliton can be guided following an arbitrary traje…
We demonstrate robust, stable, mobile two-dimensional (2D) dipolar ring-dark-in-bright (RDB) Bose-Einstein condensate (BEC) solitons for repulsive contact interaction, subject to a harmonic trap along the $y$ direction perpendicular to the polarization direction $z$. Such a RDB soliton has a ring-shaped notch (zero in density) imprinted on a 2D bright soliton free to move in the $x-z$ plane. At medium velocity the head-on collision of two such solitons is found to be quasi elastic with practically no deformation. The possibility of creating the RDB soliton by phase imprinting is demonstrated. …
We present experimental and numerical data on the supercontinuum generation in an optical fiber pumped in the normal dispersion range where the seeded dark and the spontaneously generated bright solitons contribute to the spectral broadening. We report the dispersive radiation arising from the interaction of the bright and dark solitons. This radiation consists of the two weak dispersing pulses that continuously shift their frequencies and shape the short and long wavelength wings of the supercontinuum spectrum.
A study of bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is investigated. Formation of soliton trains in the quasi one-dimensional confinement is shown. Additionally, fragmentation of a BEC has been observed outside confinement, in free space. In the end a double BEC production setup for studying soliton collisions is described.
In this paper, we succeed to bilinearize the $\cal{PT}$-invariant nonlocal nonlinear Schrödinger (NNLS) equation through a nonstandard procedure and present more general bright soliton solutions. We achieve this by bilinearizing both the NNLS equation and its associated parity transformed complex conjugate equation in a novel way. The obtained one and two soliton solutions are invariant under combined space and time reversal transformations and are more general than the known ones. Further, by considering the two-soliton solution we bring out certain novel interaction properties of the $\cal{P…
We analyze a possibility of macroscopic quantum effects in the form of coupled structural oscillations and shuttle motion of bright two-component spin-orbit-coupled striped (one-dimensional, 1D) and semi-vortex (two-dimensional, 2D) matter-wave solitons, under the action of linear mixing (Rabi coupling) between the components. In 1D, the intrinsic oscillations manifest themselves as flippings between spatially even and odd components of striped solitons, while in 2D the system features periodic transitions between zero-vorticity and vortical components of semi-vortex solitons. The consideratio…
