Topological oscillated edge states in trimer lattices.

We investigate a 1D trimer optical lattice model. Two kinds of topological oscillating optical transmission phenomena at edges are shown. The exact and the approximate solutions of the system's edge states are obtained with and without the inversion symmetry for this system respectively.

Versatile Gold Telluride Iodide Monolayer as a Potential Photocatalyst for Water Splitting.

Two-dimensional materials promise great potential for photochemical water splitting due to the abundant active sites and large surface area, but few of the known materials meet the rigorous requirements. In this work, we systematically investigate structural, electronic, and optical properties of an experimentally unexplored 2D material, i.e.

Magnetic lump motion in saturated ferromagnetic films.

In this paper, we study in detail the nonlinear propagation of a magnetic soliton in a ferromagnetic film. The sample is magnetized to saturation by an external field perpendicular to film plane. A generalized (2+1)-dimensional short-wave asymptotic model is derived.

Modified linear stability analysis for quantitative dynamics of a perturbed plane wave.

We develop linear stability analysis (LSA) to quantitatively predict the dynamics of a perturbed plane wave in nonlinear systems. We take a nonintegrable fiber model with purely fourth-order dispersion as an example to demonstrate this method's effectiveness. For a Gaussian-type initial perturbation with cosine-type modulation on a plane wave, its propagation velocities, periodicity, and localization are predicted successfully, and the range of application is discussed.

High-order rogue waves excited from multi-Gaussian perturbations on a continuous wave.

Peregrine rogue wave excitation has applications in gaining high-intensity pulses, etc., and a high-order rogue wave exhibits higher intensity. An exact solution and collision between breathers are two existing ways to excite high-order ones.

Dynamics of perturbations at the critical points between modulation instability and stability regimes.

We study numerically the evolutions of perturbations at critical points between modulational instability and stability regimes. It is demonstrated that W-shaped solitons and rogue waves can be both excited from weak resonant perturbations at the critical points. The rogue wave excitation at the critical points indicates that rogue wave comes from modulation instability with resonant perturbations, even when the baseband modulational instability is absent.

Excitation conditions of several fundamental nonlinear waves on continuous-wave background.

We study the excitation conditions of antidark solitons and nonrational W-shaped solitons in a nonlinear fiber with both third-order and fourth-order effects. We show that the relative phase can be used to distinguish antidark solitons and nonrational W-shaped solitons. The excitation conditions of these well-known fundamental nonlinear waves (on a continuous-wave background) can be clarified clearly by the relative phase and three previously reported parameters (background frequency, perturbation frequency, and perturbation energy).

Growth rate of modulation instability driven by superregular breathers.

We report an exact link between Zakharov-Gelash super-regular (SR) breathers (formed by a pair of quasi-Akhmediev breathers) with interesting different nonlinear propagation characteristics and modulation instability (MI). This shows that the absolute difference of group velocities of SR breathers coincides exactly with the linear MI growth rate. This link holds for a series of nonlinear Schrödinger equations with infinite-order terms.

Mechanism of Kuznetsov-Ma breathers.

We discuss how to understand the dynamical process of Kuznetsov-Ma breather, based on some basic physical mechanisms. It is shown that the dynamical process of Kuznetsov-Ma breather involves at least two distinctive mechanisms: modulational instability and the interference effects between a bright soliton and a plane-wave background. Our analysis indicates that modulational instability plays dominant roles in the mechanism of Kuznetsov-Ma breather admitting weak perturbations, and the interference effect plays a dominant role for the Kuznetsov-Ma breather admitting strong perturbations.

Several localized waves induced by linear interference between a nonlinear plane wave and bright solitons.

We investigate linear interference effects between a nonlinear plane wave and bright solitons, which are admitted by a pair-transition coupled two-component Bose-Einstein condensate. We demonstrate that the interference effects can induce several localized waves possessing distinctive wave structures, mainly including anti-dark solitons, W-shaped solitons, multi-peak solitons, Kuznetsov-Ma like breathers, and multi-peak breathers. Specifically, the explicit conditions for them are clarified by a phase diagram based on the linear interference properties.

Coherence transformations in single qubit systems.

We investigate the single qubit transformations under several typical coherence-free operations, such as, incoherent operation (IO), strictly incoherent operation (SIO), physically incoherent operation (PIO), and coherence-preserving operation (CPO). Quantitative connection has been built between IO and SIO in single qubit systems. Moreover, these coherence-free operations have a clear hierarchical relationship in single qubit systems: CPO ⊂ PIO ⊂ SIO=IO.

Generation mechanisms of fundamental rogue wave spatial-temporal structure.

We discuss the generation mechanism of fundamental rogue wave structures in N-component coupled systems, based on analytical solutions of the nonlinear Schrödinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the N-component coupled nonlinear Schrödinger equation.

Superregular breathers in a complex modified Korteweg-de Vries system.

We study superregular (SR) breathers (i.e., the quasi-Akhmediev breather collision with a certain phase shift) in a complex modified Korteweg-de Vries equation.

Soliton excitations on a continuous-wave background in the modulational instability regime with fourth-order effects.

We study the correspondence between modulational instability and types of fundamental nonlinear excitation in a nonlinear fiber with both third-order and fourth-order effects. Some soliton excitations are obtained in the modulational instability regime which have not been found in nonlinear fibers with second-order effects and third-order effects. Explicit analysis suggests that the existence of solitons is related to the modulation stability circle in the modulation instability regime, and they just exist in the modulational instability regime outside of the modulational stability circle.

Symmetric and asymmetric optical multipeak solitons on a continuous wave background in the femtosecond regime.

We study symmetric and asymmetric optical multipeak solitons on a continuous wave background in the femtosecond regime of a single-mode fiber. Key characteristics of such multipeak solitons, such as the formation mechanism, propagation stability, and shape-changing collisions, are revealed in detail. Our results show that this multipeak (symmetric or asymmetric) mode could be regarded as a single pulse formed by a nonlinear superposition of a periodic wave and a single-peak (W-shaped or antidark) soliton.

State transition induced by higher-order effects and background frequency.

The state transition between the Peregrine rogue wave and W-shaped traveling wave induced by higher-order effects and background frequency is studied. We find that this intriguing transition, described by an exact explicit rational solution, is consistent with the modulation instability (MI) analysis that involves a MI region and a stability region in a low perturbation frequency region. In particular, the link between the MI growth rate and the transition characteristic analytically demonstrates that the localization characteristic of transition is positively associated with the reciprocal of the zero-frequency growth rate.

Rogue-wave pattern transition induced by relative frequency.

We revisit a rogue wave in a two-mode nonlinear fiber whose dynamics is described by two-component coupled nonlinear Schrödinger equations. The relative frequency between two modes can induce different rogue wave patterns transition. In particular, we find a four-petaled flower structure rogue wave can exist in the two-mode coupled system, which possesses an asymmetric spectrum distribution.

Optical rogue waves generated on Gaussian background beam.

We study optical rogue waves (RWs) in a nonlinear graded-index waveguide with variable coefficients. An exact RW solution on Gaussian background beam is presented, in contrast to the previous studies about RWs, on plane wave background. It is shown that the characteristics of RWs are maintained on Gaussian background beam and that the beam's width is even a bit smaller than the RWs scale.

Dynamics of a nonautonomous soliton in a generalized nonlinear Schrödinger equation.

We solve a generalized nonautonomous nonlinear Schrödinger equation analytically by performing the Darboux transformation. The precise expressions of the soliton's width, peak, and the trajectory of its wave center are investigated analytically, which symbolize the dynamic behavior of a nonautonomous soliton. These expressions can be conveniently and effectively applied to the management of soliton in many fields.