Modulational instability of a resonantly polariton condensate in discrete lattices

We study modulational instability of a resonantly polariton condensate in a discrete lattice.Employing a discrete gain-saturation model,we derive the dispersion relation for the modulational instability by means of the linear-stability analysis.Effects of the pumping strength,the nonlinearity,the strength of the detuning,and the coupling strength on the modulation instability are investigated.It is found that the interplay between these parameters will dramatically change the modulational instability condition.We believe that the predicted results in this work can be useful for future possible experiment of exciton-polariton condensate in lattices.

Dual-wavelength pumped latticed Fermi-Pasta-Ulam recurrences in nonlinear Schrödinger equation

We show that the nonlinear stage of the dual-wavelength pumped modulation instability(MI)in nonlinear Schrödinger equation(NLSE)can be effectively analyzed by mode truncation methods.The resulting complicated heteroclinic structure of instability unveils all possible dynamic trajectories of nonlinear waves.Significantly,the latticed-Fermi-Pasta-Ulam recurrences on the modulated-wave background in NLSE are also investigated and their dynamic trajectories run along the Hamiltonian contours of the heteroclinic structure.It is demonstrated that there has much richer dynamic behavior,in contrast to the nonlinear waves reported before.This novel nonlinear wave promises to inject new vitality into the study of MI.

Parametric instability in the pure-quartic nonlinear Schrödinger equation

We study the nonlinear stage of modulation instability(MI)in the non-intergrable pure-quartic nonlinear Schrödinger equation where the fourth-order dispersion is modulated periodically.Using the three-mode truncation,we reveal the complex recurrence of parametric resonance(PR)breathers,where each recurrence is associated with two oscillation periods(PR period and internal oscillation period).The nonlinear stage of parametric instability admits the maximum energy exchange between the spectrum sidebands and central mode occurring outside the MI gain band.

Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas

By one-dimensional particle-in-cell(PIC) simulations, the propagation and stability of relativistic electromagnetic(EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas.The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 10^(23) m^(-3) and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases(decreases) with the increase of the carrier wave frequency(vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude.This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.

Phase-matching analysis of four-wave mixing induced by modulation instability in a single-mode fiber

Four-wave mixing induced by modulation instability in a single-mode fiber is analyzed from the phase-matching point of view. For the two-channel transmission, a method is proposed to select the four-wave-mixing-induced sidebands, which is based on the proper use of a continuous-wave and a pulse as light sources. We find that a mass of sidebands are generated in the modulation instability resonance region, and the power of the sideband increases with not only the peak power of the pump pulse but also the continuous-wave power which acts as a seed. The research will provide guidance for fiber communication and sensing systems using wavelength division multiplexing technology.

Modulational Instability of Trapped Two-Component Bose-Einstein Condensates

The modulational instability of two-component Bose-Einstein condensates(BECs)under an external parabolic potential is discussed.Based on the trapped two-component Gross-Pitaevskill equations,a time-dependent dispersion relation is obtained analytically by means of the modified lens-type transformation and linear stability analysis.It is shown that a modulational unstable time scale exists for trapped two-component BECs.The modulational properties-which are determined by the wave number,external trapping parameter,intraand inter-species atomic interactions-are modified significantly.The analytical results are confirmed by direct numerical simulation.Our results provide a criterion for judging the occurrence of instability of the trapped two-component BECs in experiment.

Numerical simulation on modulational instability of ion-acoustic waves in plasma

In this paper, the one-dimensional(1D) particle-in-cell(PIC) simulation is used to study the modulation instability of ion acoustic waves in electron–ion plasmas. The ion acoustic wave is described by using a nonlinear Schr¨odinger equation(NLSE) derived from the reductive perturbation method. Form our numerical simulations, we are able to demonstrate that,after the modulation, the amplitude increases steadily over time. Furthermore, by comparing the numerical results with traditional analytical solutions, we acquire the application scope for the reductive perturbation method to obtain the NLSE.We also find this method can also be extended to other fields such as fluid dynamics, nonlinear optics, solid state physics,and the Bose–Einstein condensate to validate the application scope of the results from the traditional perturbation method.

Experimental study on modulational instability and evolution of crescent waves

A series of experiments on the instability of steeP water wave trains in water with finite water depths and infinite water depths in a wide wave basin were performed. It was found that under the coupled development of modulational instability and class-Ⅱ instability, the initial two-dimensional steep wave trains evolved into three＇dimensional crescent waves, followed by the occurrence of disordered water surfaces, and that the wave energy transferred to sidebands in the amplitude spectrum of the water surface elevation. The results also show that water depth has a significant effect on the growth of modulational instability and the evolutiin of crescent waves. The larger the water depth, the more quickly the modulational instability suppresses class-II instability.

Modulational instability of incoherently coupled beams in azobenzene-containing polymer with photoisomerization nonlinearity

The modulational instability of two incoherently coupled beams in azobenzene-containing polymer with photoisomerization nonlinearity is investigated analytically and numerically. Our results show that as a precursor to spatial optical soliton formation, modulational instability can be adjusted and controlled by the wavelength combinations of the signal and background beams. We also discuss the dependences of strength of modulational instability on intensities of two signal beams and background beam. These findings make it possible to predict the formation of incoherently coupled soliton pairs in azobenzene-containing polymer.

Modulational instability of the coupled waves between fast magnetosonic wave and slow Alfvén wave in the laser–plasma interaction

By performing modulational instability analysis of the the nonlinear coupled dimensionless equations between a fast magnetosonic wave(FMSW)propagating obliquely with the magneticfield and a low-frequency slow Alfvén wave(SAW),we obtain the dispersion relation of the perturbation wave.The growth rate of the perturbation wave is obtained.It is found that the growth rate increases as background magnetic field increases,which is in agreement with that reported by Tiwary et al(2016 Phys.Plasmas 23122307).A critical perturbation wave number is found.When the perturbation wave number is greater than or equal to the critical value,the growth rate is positive and it increases as the perturbation wave number increases,while the wave is stable.The maximum growth rate is reached when the frequency of the FMSW is half of the ion cyclotron frequency.The minimum growth rate is reached when the propagation direction of the perturbation wave is the same as that of the FMSW.

Discrete modulational instability and bright localized spin wave modes in easy-axis weak ferromagnetic spin chains involving the next-nearest-neighbor coupling

We report a theoretical work on the properties of modulational instability and bright type nonlinear localized modes in one-dimensional easy-axis weak ferromagnetic spin lattices involving next-nearest-neighbor couplings.With a linear stability analysis, we calculate the growth rates of the modulational instability, and plot the instability regions.When the strength of the next-nearest-neighbor coupling is large enough, two new asymmetric modulational instability regions appear near the boundary of the first Brillouin zone.Furthermore, analytical forms of the bright nonlinear localized modes are constructed by means of a quasi-discreteness approach.The influence of the next-nearest-neighbor coupling on the Brillouin zone center mode and boundary mode are discussed.In particular, we discover a reversal phenomenon of the propagation direction of the Brillouin zone boundary mode.

Development of cancer-initiating cells and immortalized cells with genomic instability

Cancers that develop after middle age usually exhibit genomic instability and multiple mutations. This is in direct contrast to pediatric tumors that usually develop as a result of specific chromosomal translocations andepigenetic aberrations. The development of genomic instability is associated with mutations that contribute to cellular immortalization and transformation. Cancer occurs when cancer-initiating cells(CICs), also called cancer stem cells, develop as a result of these mutations. In this paper, we explore how CICs develop as a result of genomic instability, including looking at which cancer suppression mechanisms are abrogated. A recent in vitro study revealed the existence of a CIC induction pathway in differentiating stem cells. Under aberrant differentiation conditions, cells become senescent and develop genomic instabilities that lead to the development of CICs. The resulting CICs contain a mutation in the alternative reading frame of CDKN2A(ARF)/p53 module, i.e., in either ARF or p53. We summarize recently established knowledge of CIC development and cellular immortality, explore the role of the ARF/p53 module in protecting cells from transformation, and describe a risk factor for genomic destabilization that increases during the process of normal cell growth and differentiation and is associated with the downregulation of histone H2 AX to levels representative of growth arrest in normal cells.

Optimization control of modulation-instability gain in photonic crystal fibres with two zero-dispersion wavelengths

We design three kinds of photonic crystal fibres （PCF） with two zero-dispersion wavelengths （ZDWs） using the improved full vector index method （FVIM） and finite-difference frequency domain （FDFD} techniques. Based on these designed fibres, the effect of fibre structure, pump power and wavelength on the modulation instability （MI） gain in the anomalous dispersion region close to the second ZDW of the PCFs is comprehensively analysed in this paper. The analytical results show that an optimal MI gain can be obtained when the optimal pump wavelength （1530 nm） is slightly shorter than the second ZDW （1538 nm） and the optimal pump power is 250 W. Importantly, the total MI gain bandwidth has been increased to 260 nm for the first time, so far as we know, for an optimally-designed fibre with ∧ = 1.4 nm and d/∧ = 0.676, and the gain profile became much smoother. The optimal pump wavelength relies on the second ZDW of the PCF whereas the optimal pump power depends on the corporate operation of the optimal fibre structure and optimal pump wavelength, which is important in designing the most appropriate PCF to attain higher broadband and gain amplification.

Modulational instability, quantum breathers and two-breathers in a frustrated ferromagnetic spin lattice under an external magnetic field

The modulational instability, quantum breathers and two-breathers in a frustrated easy-axis ferromagnetic zig-zag chain under an external magnetic field are investigated within the Hartree approximation. By means of a linear stability analysis, we analytically study the discrete modulational instability and analyze the effect of the frustration strength on the discrete modulational instability region. Using the results from the discrete modulational instability analysis, the presence conditions of those stationary bright type localized solutions are presented. On the other hand, we obtain the analytical expressions for the stationary bright localized solutions and analyze the effect of the frustration on their emergence conditions. By taking advantage of these bright type single-magnon bound wave functions obtained, quantum breather states in the present frustrated ferromagnetic zig-zag lattice are constructed. What is more, the analytical forms for quantum two-breather states are also obtained. In particular, the energy level formulas of quantum breathers and two-breathers are derived.

Modulational instability for a self-attractive two-component Bose-Einstein condensate

By means of the multiple-scale expansion method, the coupled nonlinear Schrgdinger equations without an explicit external potential are obtained in two-dimensional geometry for a self-attractive Bose-Einstein condensate composed of different hyperfine states. The modulational instability of two-component condensate is investigated by using a simple technique. Based on the discussion about two typical cases, the explicit expression of the growth rate for a purely growing modulational instability and the optimum stable conditions are given and analysed analytically. The results show that the modulational instability of this two-dimensional system is quite different from that in a one-dimensional system.

Relativistic degenerate effects of electrons and positrons on modulational instability of quantum ion acoustic waves in dense plasmas with two polarity ions

The nonlinear propagation of quantum ion acoustic wave（QIAW） is investigated in a four-component plasma composed of warm classical positive ions and negative ions,as well as inertialess relativistically degenerate electrons and positrons.A nonlinear Schrodinger equation is derived by using the reductive perturbation method,which governs the dynamics of QIAW packets.The modulation instability analysis of QIAWs is considered based on the typical parameters of the white dwarf.The results exhibit that both in the weakly relativistic limit and in the ultrarelativistic limit,the modulational instability regions are sensitively dependent on the ratios of temperature and number density of negative ions to those of positive ions respectively,and on the relativistically degenerate effect as well.

Impact of Quantum Fluctuations on the Modulational Instability of a Modified Gross-Pitaevskii Equation with Two-Body Interaction

Modulational instability conditions for the generation of localized structures in the context of matter waves in Bose-Einstein condensates are investigated analytically and numerically. The model is based on a modified Gross-Pitaevskii equation, which account for the energy dependence of the two-body scattering amplitude. It is shown that the modified term due to the quantum fluctuations modify significantly the modulational instability gain. Direct numerical simulations of the full modified Gross-Pitaevskii equation are performed, and it is found that the modulated plane wave evolves into a train of pulses, which is destroyed at longer times due to the effects of quantum fluctuations.

Modulational Instability of Ion—Acoustic Waves in a Warm Plasma with a Relativistic Electron Beam

The modulational instability of ion-acoustic wave in a collisionless, unmagnetized plasma consisting of warm ions, hot isothermal electrons, and relativistic electron beam is studied. A modified nonlinear Schr?dinger equation including one additional term that comes from the effect of relativistic electron beam is derived. It is found that the inclusion of a relativistic electron beam would modify the modulational instability of the wave packet and could not admit any stationary soliton waves.

Propagation and modulational instability of Rossby waves in stratified fluids

Perturbation analysis and scale expansion are used to derive the(2+1)-dimensional coupled nonlinear Schr¨odinger(CNLS)equations that can describe interactions of two Rossby waves propagating in stratified fluids.The(2+1)-dimensional equations can reflect and describe the wave propagation more intuitively and accurately.The properties of the two waves in the process of propagation can be analyzed by the solution obtained from the equations using the Hirota bilinear method,and the influence factors of modulational instability are analyzed.The results suggest that,when two Rossby waves with slightly different wave numbers propagate in the stratified fluids,the intensity of bright soliton decreases with the increases of dark soliton coefficients.In addition,the size of modulational instable area is related to the amplitude and wave number in y direction.

Modulational Instability of Optical Vortices in Engineered Saturable Media

Propagation of light beams in turbid media such as underwater environments,fog,clouds,or biological tissues finds increasingly important applications in science and technology,including bio-imaging,underwater communication,and free-space communication technologies.While many of these applications traditionally relied on conventional,linearly polarized Gaussian beams,light possesses many degrees of freedom that are still largely unexplored,such as spin angular momentum(SAM)and orbital angular momentum(OAM).Here,we present nonlinear light-matter interactions of such complex light beams with"rotational"degrees of freedom in engineered nonlinear colloidal media.By making use of both variational and perturbative approach,we consider non-cylindrical optical vortices,elliptical optical vortices,and higher-order Bessel beams integrated in time(HOBBIT)to predict the dynamics and stability of the evolution of these beams.These results may find applications in many scenarios involving light transmission in strongly scattering environments.