Quantized Superfluid Vortex Filaments Induced by the Axial Flow Effect

We report the quantized superfluid vortex filaments induced by the axial flow effect, which exhibit intriguing loop structures on helical vortexes. Such new vortex filaments correspond to a series of soliton excitations including the multipeak soliton, W-shaped soliton, and anti-dark soliton, which have no analogue when the axial flow effect is absent. In particular, we show that the vortex filaments induced by the multipeak soliton and W-shaped soliton arise from the dual action of bending and twisting of the vortex, while the vortex filament induced by the anti-dark soliton is caused only by the bending action, which is consistent with the case of the standard bright soliton. These results will deepen our understanding of breather-induced vortex filaments and will be helpful for controllable ring-like excitations on vortices.     

Different Kinds of Discrete Breathers in Three Types of One-Dimensional Models

The dynamics of different kinds of discrete breathers in three types of one-dimensional monatomic chains with on-site and inter-site potentials are investigated. The existence and evolution of symmetric breather, antisymmetric breather, and multibreather in one-dimensional models are proved by using rotating wave approximation, local anharmonic approximation, and the numerical method. The linear stability of these breathers is investigated by using Lyapunov stable analysis. The localization and stability of breathers in three types of models correlate closely to the system nonlinear parameter β.     

Breather Interaction Properties Induced by Self-Steepening and Space-Time Correction

We study the properties of breather interactions in nonlinear Kerr media with self-steepening and space-time correction and with either self-focusing or self-defocusing nonlinearity, and present a new family of exact breather solutions via the Darboux transformation with a special-designed quadratic spectral parameter. In contrast to the previous results of the nonlinear Schr?dinger equation(NLSE) hierarchy, we show that the relative phase of colliding breathers has a significant effect on the collision manifestation. In particular, only the out-of-phase interactions can generate small amplitude waves at the collision center, which are analogous to the NLSE superregular breathers. Our results will deepen our understanding of the properties of breather interactions and they will offer the possibility of experimental observations of super-regular breather dynamics in systems with self-steepening and space-time correction.     

Two-Dimensional Breather Lattice Solutions and Compact-Like Discrete Breathers and Their Stability in Discrete Two-Dimensional Monatomic β-FPU Lattice

We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for two- dimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry＇s linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete two- dimensional monatomic β-FPU lattice.     

Interaction region of magnon-mediated spin torques and novel magnetic states

We determine the region in which the magnon-mediated spin torques exist. This region can be controlled by the spin waves. In terms of stability analysis of magnetization dynamics based on the spin-wave background, we obtain the instability conditions of spin waves. With these results, we find the relationship between unstable regions and the formation of Akhmediev breather, Kuznetsov–Ma breather and rogue waves. We establish the phase diagram of some novel magnetic excitaions.     

Discrete Breathers in Lattices of Coupled Oscillators

Discrete breathers are generic solutions for the dynamics of nonlinearly coupled oscillators. We show that discrete breathers can be observed in low-dimensional and high-dimensional lattices by exploring the sinusoidally coupled pendulum. Loss of stability of the breather solution is studied. We also find the existence of discrete breather in lattices with parameter mismatches. Breather phase synchronization is exhibited for the coupled chaotic oscillators.     

Dynamics of breathers and rogue waves in scalar and multicomponent nonlinear systems

In this paper, we propose a new method, the variable separation technique, for obtaining a breather and rogue wave solution to the nonlinear evolution equation. Integrable systems of the derivative nonlinear Schrödinger type are used as three examples to illustrate the effectiveness of the presented method. We then obtain a family of rational solutions. This family of solutions includes the Akhmediev breather, the Kuznetsov-Ma breather, versatile rogue waves, and various interactions of localized waves. Moreover, the main characteristics of these solutions are discussed and some graphics are presented. More importantly, our results show that more abundant and novel localized waves may exist in the multicomponent coupled equations than in the uncoupled ones.     

Discrete breathers

Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurrence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattices — quantum breathers.Finally we will formulate a new conceptual approach capable of predicting whether discrete breathers exist for a given system or not, without actually solving for the breather. We discuss potential applications in lattice dynamics of solids (especially molecular crystals), selective bond excitations in large molecules, dynamical properties of coupled arrays of Josephson junctions, and localization of electromagnetic waves in photonic crystals with nonlinear response.     

Discrete soliton collisions in a waveguide array with saturable nonlinearity

We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable nonlinearity. The saturability allows the existence of mobile breathers with high power. Three main regimes are observed: breather fusion, breather reflection and breather creation. The last regime seems to be exclusive of systems with a saturable nonlinearity, and has been previously observed in continuous models. In some cases a “symmetry breaking” can be observed, which we show to be an numerical artifact.     

锁模光纤激光器时变动力学

锁模激光器除了可以产生稳定的超短脉冲以外,还可产生一系列重要的非平衡态动力学过程.这些快速变化的动力学过程有助于理解超快激光器和相关非线性系统的动力学,也对超快激光器的稳定性设计有重要指导意义.随着超快探测技术的发展,锁模激光器超快动力学的研究取得了一系列突破.介绍了锁模激光器几个典型的非平衡态动力学过程,包括锁模启动...     

Kink-like breathers in Bose–Einstein condensates with helicoidal spin–orbit coupling

We report a kind of kink-like breathers in one-dimensional Bose–Einstein condensates (BECs) with helicoidal spin–orbit coupling (SOC), on whose two sides the background densities manifest obvious difference (called kink amplitude). The kink amplitude and shape of breather can be adjusted by the strength and period of helicoidal SOC, and its atomic number in two components exchanges periodically with time. The SOC has similar influence on the kink amplitude and the exchanged atomic number, especially when the background wave number is fixed. It indicates that the oscillating intensity of breather can be controlled by adjusting initial kink amplitude. Our work showcases the great potential of realizing novel types of breathers through SOC, and deepens our understanding on the formation mechanisms of breathers in BECs.     

Superregular breathers and state transitions in a resonant erbium-doped fiber system with higher-order effects

In this paper, we concentrate on the Hirota and Maxwell-Bloch (HMB) system governing the propagation of the femtosecond pulse in an erbium doped fiber. We present the superregular breather solutions that are nonlinear superposition of a pair of travelling breathers propagating in opposite directions. We further study the full- and half-transition modes of the superregular breather solution, which appears as a result of the coupled and higher-order effects. These waves reduce to small localized perturbations of the background at time zero.     

Energy transfer in weakly coupled nonlinear oscillator chains: Transition from a wandering breather to nonlinear self-trapping

We present analytical and numerical studies of phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different dynamical regimes of the coupled breathers, either immovable or slowly moving: the periodic wandering of the low-amplitude breather between the chains, and the one-chain-localization of the high-amplitude breather. These two modes of coupled breathers can be mapped exactly onto two solutions of a pendulum equation, detached by a separatrix mode. We also show that these two regimes of the coupled breathers are similar, and are described by a similar pair of equations, to the two regimes in the nonlinear tunneling dynamics of two weakly coupled Bose-Einstein condensates. On the basis of this analogy, we predict a new tunneling mode of two weakly coupled Bose-Einstein condensates in which their relative phase oscillates around π/2 modulo π.     

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.     

Bound states of breathers in the Frenkel-Kontorova model

In the dissipative, driven standard Frenkel-Kontorova model propagating breathers exist as attractors of the dynamics. In collisions, these excitations interact through the phonons they emit. A possible result of a two-breather collision is a bound state of two breathers. After looking at phonons and breather collisions, we present phenomenological results on breather bound states obtained from lattice dynamics simulations. In particular, we find that bound states can be characterised by the distance between the two breathers they comprise and their propagation velocity. Contrary to the single breather case, several values of the propagation velocity are easily accessible to bound states at fixed model parameters. The results are interpreted on the basis of the observed phonon spectra. The latter can easily be explained as Doppler-shifted combination frequencies of breather harmonics and a discreteness-induced perturbation frequency.Received: 18 December 2003, Published online: 15 March 2004PACS: 63.20.Ry Anharmonic lattice modes - 63.20.Pw Localized modes     

Wave scattering by discrete breathers

We present a theoretical study of linear wave scattering in one-dimensional nonlinear lattices by intrinsic spatially localized dynamic excitations or discrete breathers. These states appear in various nonlinear systems and present a time-periodic localized scattering potential for plane waves. We consider the case of elastic one-channel scattering, when the frequencies of incoming and transmitted waves coincide, but the breather provides with additional spatially localized ac channels whose presence may lead to various interference patterns. The dependence of the transmission coefficient on the wave number q and the breather frequency Omega(b) is studied for different types of breathers: acoustic and optical breathers, and rotobreathers. We identify several typical scattering setups where the internal time dependence of the breather is of crucial importance for the observed transmission properties.     

Discrete gap breathers in a diatomic K2-K3-K4 chain with cubic nonlinearity

The discrete gap breathers （DGBs） in a one-dimensional diatomic chain with K2-K3-K4 potential are analysed. Using the local anharmonicity approximation, the analytical investigation has been implemented. The dependence of the central amplitude of the discrete gap breathers on the breather frequency and the localization parameter are calculated. With increasing breather frequency, the DGB amplitudes decrease. As a function of the localization parameter, the central amplitude exhibits bistability, corresponding to the two branches of the curve ω = ω（ζ）. With a nonzero cubic term, the HS mode of DGB profiles becomes weaker. With increasing K3, the HS mode of DGB profiles becomes weaker and a bit narrower. For the LS mode, with increasing K3, the central particle amplitude becomes larger, and the DGB profile becomes much sharper. But, as k3 increases further, the central particle amplitude of the LS mode becomes smaller.     

The notion of persistence applied to breathers in thermal equilibrium

We study the thermal equilibrium of nonlinear Klein-Gordon chains at the limit of small coupling (anticontinuum limit). We show that the persistence distribution associated to the local energy density is a useful tool to study the statistical distribution of the so-called thermal breathers, mainly when the equilibrium is characterized by long-lived pinned excitations; in that case, the distribution of persistence intervals turns out to be a power law. We demonstrate also that this generic behaviour has a counterpart in the power spectra, where the high-frequencies domains nicely collapse if properly rescaled. These results are also compared to nonlinear Klein-Gordon chains with a soft nonlinearity, for which the thermal breathers are rather mobile entities. Finally, we discuss the possibility of a breather-induced anomalous diffusion law, and show that despite a strong slowing down of the energy diffusion, there are numerical evidences for a normal asymptotic diffusion mechanism, but with exceptionally small diffusion coefficients.     

椭圆响应强非局域非线性介质中的二维异步分数傅里叶变换及光束传输特性

研究了椭圆响应强非局域非线性介质中的光束传输问题. 结果表明:任意光束在这类介质中传输时均遵守二维异步分数傅里叶变换的传输规律. 基于二维异步分数傅里叶变换这一数学工具, 可很方便地对光束的传输进行解析求解并分析其性质. 利用二维异步分数傅里叶变换的性质, 讨论了一般光束的传输性质; 分析了孤子和二维异步呼吸子的形成条件; 得出了孤子/呼吸子的相互作用规律. 关键词： 椭圆响应 强非局域非线性 孤子 呼吸子     

High-order breather,M-kink lump and semi-rational solutions of potential Kadomtsev-Petviashvili equation

N-kink soliton and high-order synchronized breather solutions for potential Kadomtsev-Petviashvili equation are derived by means of the Hirota bilinear method,and the limit process of high-order synchronized breathers are shown.Furthermore,M-lump solutions are also presented by taking the long wave limit.Additionally,a family of semi-rational solutions with elastic collision are generated by taking a long-wave limit of only a part of exponential functions,their interaction behaviors are shown by three-dimensional plots and contour plots.