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Highlights • The Akhmediev breather (AB) solutions for the vector nonlinear Schrödinger equation (VNLSE) are constructed by the Darboux transformation. • We develop a method to determine the spectral curve where the AB solutions are located. • The high order rogue waves (RWs), multi-RWs and multi-high order RWs are derived by Darboux transformation. • We find the dispersion equation for the MI is equivalent with determined equation for ABs or RWs. Abstract Modulational instability has been used to explain the formation of breathers and rogue waves qualitatively. In this paper, we show modulational instability can be used to explain the structure of them in a quantitative way. In the first place, we develop a method to derive general forms for Akhmediev breathers, rogue waves and their multiple or high order ones in a N -component nonlinear Schrödinger equations. The existence condition for each pattern is clarified clearly with a compact algebraic equation. Moreover, we show that the existence condition of ABs and RWs is consistent with the dispersion relation of the linear stability analysis on the background solution. The results further deepen our understanding on the quantitative relations between modulational instability and homoclinic orbits solutions. [ABSTRACT FROM AUTHOR]

Highlights • Dark solitons are derived on a stripe phase background. • Many different profiles are admitted by the soliton. • The interactions between them are investigated analytically. Abstract We present dark solitons on stripe phase background in a two-component coupled Bose-Einstein condensate. It is demonstrated that there are many different dark soliton profiles, in contrast to the dark solitons reported before. These different profiles are classified qualitatively to four distinctive cases, according to the differences between stripe spatial period and soliton size, and the fluctuation degree of stripe background. The interactions between these different dark solitons are also investigated. These results further enrich our knowledge on dark solitons in ultra-cold atomic systems, and other coupled nonlinear systems. [ABSTRACT FROM AUTHOR]

Transition dynamics have been studied widely in two-mode Bose–Einstein condensate systems with linear coupling effects. Nonlinear interaction between atoms would induce a nonlinear Josephson oscillation, which admits an oscillation form different from the classical Josephson oscillation. Similar extensions for the Rosen–Zener transition and the Landau–Zener transition also suggest that a strong nonlinear strength would induce nonlinear-type transition dynamics, which is in sharp contrast to the linear process. Interestingly, here we show a standard Josephson oscillation that has a constant linear coupling strength, no matter how great the nonlinear interaction strength is. This characteristic is in sharp contrast to the nonlinear Josephson oscillation reported before in nonlinear coupled systems. By manipulating the linear coupling strength with the RF field, we demonstrate that the Rosen–Zener transition particles, with an invariant distribution profile, can be managed well under exponential and periodic forms. The nonlinear interaction strength is found to have no effect on the transition rate between atoms in the two components for the case where the inter- and intra-atomic interaction strengths are equal. Furthermore, we test the robustness of the transition dynamics against parameter deviations and noises in the initial condition. These results are helpful for controllable quantum state preparations.

We study rogue wave excitation pattern in a two-component Bose-Einstein condensate with pair-transition effects. The results indicate that rogue wave excitation can exist on a stripe phase background for which there are cosine and sine wave background in the two components respectively. The rogue wave peak can be much lower than the ones of scalar matter wave rogue waves, and varies with the wave period changing. Both rogue wave pattern and rogue wave number on temporal-spatial plane are much more abundant than the ones reported before. Furthermore, we prove that the rogue wave number can be n ( n + 1 ) / 2 + m ( m + 1 ) / 2 (where m, n are arbitrary non-negative integers), in contrast to n ( n + 1 ) / 2 for scalar nonlinear Schrödinger equation described systems. These results would enrich our knowledge on nonlinear excitations in multi-component Bose-Einstein condensate with transition coupling effects. [ABSTRACT FROM AUTHOR]

We study the relations between modulational instability and several well-known nonlinear excitations in a nonlinear fiber such as bright soliton, nonlinear continuous wave, Akhmediev breather, Peregrine rogue wave, and Kuznetsov–Ma breather. We present a quantitative correspondence between them based on the dominant frequency and propagation constant of each perturbation on a continuous-wave background. We especially demonstrate that rogue wave comes from modulational instability with the resonance perturbation on continuous-wave background. The numerical simulations are performed to test these theoretical results. These results will deepen our understanding of rogue wave excitation and be helpful for controllable nonlinear wave excitations in nonlinear fiber and other nonlinear systems.

A binary Mg-4Zn alloy was fabricated as a potential degradable biomaterial. To improve the corrosion resistance of Mg-4Zn alloy, an amorphous micro-arc oxidation (MAO) coating was prepared on the Mg-4Zn substrate. Electrochemical measurements and immersion tests were employed to evaluate the corrosion resistance of the specimen in simulated body fluid (SBF). Electrochemical measurements show that the Mg-4Zn alloy covered with a MAO coating has a much lower corrosion current density and a much greater polarization resistance. Immersion tests suggest that the degradation of Mg-4Zn substrate is relatively serious during the initial 8 h of immersion although it has been protected by a MAO coating. When most micro-pores within the MAO coating have been filled with precipitates resulted from the corrosion of the metal substrate, the degradation of the Mg-4Zn substrate is significantly delayed.

We derive generalized localized wave solution formula for mixed coupled nonlinear Schödinger equations (mCNLSE) by performing the unified Darboux transformation. Based on the dynamical behavior of solution, the classification of the localized wave solutions on the nonzero background is given explicitly. Especially, the parameter conditions for breather, dark soliton and rogue wave solution of mCNLSE are given in detail. Moreover, we analyze the interaction between dark soliton solution and breather solution. These results would be helpful for nonlinear localized wave excitations and applications in vector nonlinear systems. [ABSTRACT FROM AUTHOR]

We investigate localized waves of coupled two-mode nonlinear Schrödinger equations with a pair-tunneling term representing strongly interacting particles can tunnel between the modes as a fragmented pair. Facilitated by Darboux transformation, we have derived exact solution of nonlinear vector waves such as bright solitons, Kuznetsov–Ma soliton, Akhmediev breathers and rogue waves and demonstrated their interesting temporal–spatial structures. A phase diagram that demarcates the parameter ranges of the nonlinear waves is obtained. Possibilities to observe these localized waves are discussed in a two species Bose–Einstein condensate. [ABSTRACT FROM AUTHOR]

We investigate the properties of phase transitions in a weakly coupled ultracold atom-molecule boson system based on the phase space analysis approach. We identify the pure molecular and mixed atom-molecule phases of the system by different values of the time average of molecular population. When applying a periodic modulation on the energy detuning, we find that the atom-molecule mixing dynamics can be well controlled. For both high- and low-frequency modulations, it is shown that the transition points can be shifted effectively by choosing parameters of the periodic modulation appropriately. The analytical expressions for the dependence of the transition parameters on the modulation parameters are also obtained for the two cases. In particular, when the modulation with a frequency near the atom-molecule transition frequency is applied, the resonance between the periodic modulation and atom-molecule Rabi oscillation will emerge, which can affect the atom-molecule mixing dynamics dramatically and lead to the complex chaos phenomenon.

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. These results may raise the possibility of related experiments and potential applications in nonlinear optics.

We find that diverse nonlinear waves, such as soliton, Akhmediev breather, and rogue waves (RWs), can emerge and interplay with each other in a two-mode coupled system. It provides a good platform to study interaction between different kinds of nonlinear waves. In particular, we obtain dark RWs analytically for the first time in the coupled system, and find that two RWs can appear in the temporal-spatial distribution. Possible ways to observe these nonlinear waves are discussed.

One new type metastable β-titanium-alloy for biomedical applications Ti-25Nb-2Mo-4Zr (wt %) with lower elastic modulus was designed based on the d-electron alloy design method and prepared in this study. The microstructure and basic mechanical properties of designed alloy were investigated in this paper. The test results show that the Yang’s modulus is 65GPa and the tensile strength is 863MPa of designed alloy after solution treatment at 700℃ for 0.5 h; the Yang’s modulus is 68GPa and the tensile strength is 1032MPa for the designed alloy after aging treatment at 500℃ for 2 h. The designed alloy with lower Yang’s modulus is expected to have good prospects for implant biomaterials for its excellent biomechanical compatibility.

We present a series of chirp-free and chirped analytical nonautonomous soliton solutions to the generalized nonlinear Schrödinger equation with distributed coefficients by Darboux transformation from a trivial seed. For a chirp-free nonautonomous soliton, the dispersion management term can change the motion of a nonautonomous soliton and does not affect its shape at all. Specifically, the classical optical soliton can be presented with a variable dispersion term and nonlinearity when there is no gain. For a chirped nonautonomous soliton, dispersion management can meanwhile affect the shape and motion of nonautonomous solitons. The periodic dispersion term can be used to control its “breathing” shape, and it does not affect the trajectory of a nonautonomous soliton center with a certain condition.

Magnesium and its alloys are potential biodegradable materials due to their outstanding biological performance, but their poor corrosion resistance greatly limits their applications as bone implants. This paper investigates the influence of in situ magnesium oxide coating on corrosion resistance of pure magnesium in normal saline. It was discovered by SEM that rough and porous oxide coatings were obtained on the surface of the pure magnesium after heat-treated at 400~500°C and the samples were severely corroded after immersion in 0.9 wt.% NaCl solution for 3 days. It also showed that the weight loss rates of the treated pure magnesium (TPM) samples were about 5~6 times higher than that of the untreated pure magnesium (UPM) sample. Electrochemical measurements showed that the corrosion current density (icorr) of the TPM samples was one order of magnitude higher than that of the UPM sample.

Vector solitons in Bose–Einstein condensates are usually investigated analytically with identical intra- and interatomic interactions (for an integrable model). We obtain six families of exact spin soliton solutions for nonintegrable cases, which can be used to describe spin-1 Bose–Einstein condensates. The stability analyses and numerical simulations indicate that three families of spin solitons are robust against spin-dependent interactions and white noise. We further investigate the motion of these stable spin solitons driven by external linear potentials. Their moving trajectories demonstrate that the spin solitons admit a negative–positive mass transition. Some splitting and diffusing behaviors can emerge during the motion of a spin soliton that are absent in spin- 1 / 2 systems. The collisions between spin solitons are exhibited with varying relative velocity and phase. The nonintegrable properties of the systems can give rise to weak amplitude and location oscillations after collision. These stable spin soliton excitations can be used to study the negative inertial mass of solitons, the dynamics of soliton-impurity systems, and the spin dynamics in Bose–Einstein condensates. • A decoupling method is developed to derive soliton solutions for nonintegrable cases. • Three spin solitons are stable against spin-dependent interactions and white noise. • Some intriguing behaviors can emerge during the motion of spin solitons. • Nonintegrable properties induce amplitude and location oscillations after collision. [ABSTRACT FROM AUTHOR]

Abstract: The generalized Hirota equation is solved analytically through Daubox transformation method. The properties of solitons are investigated analytically based on related expressions. We present the precise balance condition between dispersion, nonlinear parameters, third-order dispersion and time-delay effects, to get stable propagating soliton. We find a condition under which effects of the third-order dispersion and time-delaying term could be eliminated. [Copyright &y& Elsevier]