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1.
Modulational Instability of (1 + 1)-Dimensional Bose-Einstein Condensate with Three-Body Interatomic Interaction
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The modulational instability of Bose-Einstein condensate with three-body interatomic interaction and external harmonic trapping potential is investigated. Both of our analytical and numerical results show that the external potential will either cause the excitation of modulationally unstable modes or restrain the modulationally unstable modes from growing. 相似文献
2.
A.B. Mikhailovskii J.G. Lominadze N.N. Erokhin N.S. Erokhin A.I. Smolyakov V.S. Tsypin 《Physics letters. A》2007
Effects of scalar nonlinearity on the generation of zonal flow by Rossby waves in shallow rotating fluid are considered. Zonal flows are generated via the action of Reynolds stress due to vector nonlinearity together with the effects of scalar nonlinearity. It is shown that the scalar nonlinearity reduces the amplitude threshold of the zonal flow instability. In addition, it increases the range of wave vectors of unstable modes subjected to the instability. The growth rate of the instability as a function of the spectrum of primary waves is calculated. The spectrum is assumed to be arbitrary with emphasizing the case of two monochromatic waves. 相似文献
3.
E. A. Kuznetsov 《JETP Letters》2017,105(2):125-129
We give a qualitative conceptual explanation of the Fermi–Pasta–Ulam (FPU) like recurrence in the onedimensional focusing nonlinear Schrodinger equation (NLSE). The recurrence can be considered as a result of the nonlinear development of the modulation instability. All known exact localized solitary wave solutions describing propagation on the background of the modulationally unstable condensate show the recurrence to the condensate state after its interaction with solitons. The condensate state locally recovers its original form with the same amplitude but a different phase after soliton leave its initial region. Based on the integrability of the NLSE, we demonstrate that the FPU recurrence takes place not only for condensate, but also for a more general solution in the form of the cnoidal wave. This solution is periodic in space and can be represented as a solitonic lattice. That lattice reduces to isolated soliton solution in the limit of large distance between solitons. The lattice transforms into the condensate in the opposite limit of dense soliton packing. The cnoidal wave is also modulationally unstable due to soliton overlapping. The recurrence happens at the nonlinear stage of the modulation instability. Due to generic nature of the underlying mathematical model, the proposed concept can be applied across disciplines and nonlinear systems, ranging from optical communications to hydrodynamics. 相似文献
4.
M.S. Ruderman 《The European physical journal. Special topics》2010,185(1):57-66
Generation of large-amplitude short-lived wave groups from small-amplitude initial perturbations in plasmas is discussed.
Two particular wave modes existing in plasmas are considered. The first one is the ion-sound wave. In a plasmas with negative
ions it is described by the Gardner equation when the negative ion concentration is close to critical. The results of numerical
solution of the Gardner equation with the modulationally unstable initial condition are presented. These results clearly show
the possibility of generation of freak ion-acoustic waves due to the modulational instability. The second wave mode is the
Alfvén wave. When this wave propagates at a small angle with respect to the equilibrium magnetic field, and its wave length
is comparable with the ion inertia length, it is described by the DNLS equation. Studying the evolution of an initial perturbation
using the linearized DNLS equation shows that the generation of freak Alfvén waves is possible due to linear dispersive focusing.
The numerical solution of the DNLS equation reveals that the nonlinear dispersive focusing can also produce freak Alfvén waves. 相似文献
5.
In addition to deep-water rogue waves which develop from the modulation instability of an optical CW, wave propagation in optical fibers may also produce shallow water rogue waves. These extreme wave events are generated in the modulationally stable normal dispersion regime. A suitable phase or frequency modulation of a CW laser leads to chirp-free and flat-top pulses or flaticons which exhibit a stable self-similar evolution. Upon collision, flaticons at different carrier frequencies, which may also occur in wavelength division multiplexed transmission systems, merge into a single, high-intensity, temporally and spatially localized rogue pulse. 相似文献
6.
The instability of small but finite amplitude waves propagating at the interface of two layers of highly conducting incompressible fluids in relative motion in presence of external uniform magnetic field is studied. Using the method of multiple scales nonlinear evolution equations are derived for both linearly stable and marginally stable cases. It is found that in the linearly stable case both the modes are modulationally unstable. The nonlinear cut-off wavenumbers are determined. 相似文献
7.
This paper analytically investigates the nonlinear behaviour of transverse plasmons in pair plasmas on the basis of the nonlinear governing equations obtained from Vlasov--Maxwell equations. It shows that high frequency transverse plasmons are modulationally unstable with respect to the uniform state of the pair plasma. Such an instability would cause wave field collapse into a localized region. During the collapse process, ponderomotive expulsion is greatly enhanced for the increase of wave field strength, leading to the formation of localized density cavitons which are significant for the future experimental research in the interaction between high frequency electromagnetic waves and pair plasmas. 相似文献
8.
Nonlinear behaviour of electron plasma waves propagating in a planar plasma-loaded waveguide immersed in an infinite magnetic field is analysed including finite temperature and mobile ion effects. It is shown that the wave becomes modulationally unstable if the wavenumber exceeds certain critical value Kc, which decreases with rise of temperature. The growth rate of instability is calculated and is found to increase with the rise of temperature. 相似文献
9.
A Hasegawa 《Physics letters. A》1975,53(1):103-104
Two (or more) quasimonochromatic waves interacting in a nonlinear dispersive medium are shown to be unstable even if each wave is modulationally stable. 相似文献
10.
Nejoh Y. 《IEEE transactions on plasma science. IEEE Nuclear and Plasma Sciences Society》1992,20(2):80-85
The association between the modified Korteweg-de Vries solitary wave and the modulationally unstable envelope solitary wave in a weakly relativistic unmagnetized plasma with trapped electrons is discussed. The effect of trapped electrons modifies the nonlinearity of the nonlinear Schrodinger equation and gives rise to the propagation of the modulationally unstable ion-acoustic solitary wave. The amplitude of the envelope solitary wave increases while the number of trapped electrons decreases. The velocity of the solitary wave decreases with increasing ionic temperature and increasing particle velocities. The ion oscillation mode, which satisfies the nonlinear dispersion relation, is also derived. The theory is applied to explain space observations of the solar energetic flows in interplanetary space and of the energetic particle events in the Earth's magnetosphere 相似文献
11.
Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system
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The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will convert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems. 相似文献
12.
In this paper,the separation-induced transition in an LPT(low-pressure turbine)cascade is investigated at low Reynolds number with DNS(direct numerical simulation).The transition process is accurately predicted giving good agreements between the DNS and experimental results.To illustrate the secondary instability of separation-induced transition in a low-disturbance environment,the results are comprehensively analyzed in both Fourier space and physical space.It is illustrated that the effect of hyperbolic instability dominates around the saddle point of hyperbolic streamlines.This instability mechanism is responsible for the emergence of the streamwise vortices in the braid region.Elongated and intensified because of the“stretching”effect of the background flow,these vortices become the most noticeable characteristic of the flow field.Fundamental modes of small spanwise wavelength are excited in the braid region,so as some low-frequency modes.The elliptical instability plays a minor role than hyperbolic instability.It is also observed that the fundamental mode with a larger spanwise wavelength is unstable in the vortex core which is associated with the deformation of the vortex core via elliptical instability.There is no convincing evidence for the existence of subharmonic instability. 相似文献
13.
Linear stability analysis of capillary instabilities in a thin nematic liquid crystalline cylindrical fiber embedded in an
immiscible viscous matrix is performed by formulating and solving the governing nemato-capillary equations, that include the
effect of temperature on the nematic ordering as well as the effect of the nematic orientation. A representative axial nematic
orientation texture with the planar easy axis at the fiber surface is studied. The surface disturbance is expressed in normal
modes, which include the azimuthal wave number m to take into account non-axisymmetric modes. Capillary instabilities in nematic fibers reflect the anisotropic nature of
liquid crystals, such as the ordering and orientation contributions to the surface elasticity and surface normal and bending
stresses. Surface gradients of normal and bending stresses provide additional anisotropic contributions to the capillary pressure
that may renormalize the classical displacement and curvature forces that exist in any fluid fiber. The exact nature (stabilizing
and destabilizing) and magnitude of the renormalization of the displacement and curvature forces depend on the nematic ordering
and orientation, i.e. the anisotropic contribution to the surface energy, and accordingly capillary instabilities may be axisymmetric or non-axisymmetric.
In addition, when the interface curvature effects are accounted for as contributions of the work of interfacial bending and
torsion to the total energy of the system, the higher-order bending moment contribution to the surface stress tensor is critical
in stabilizing the fiber instabilities. For the planar easy axis, the nematic ordering contribution to the surface energy,
which renormalizes the effect of the fiber shape, plays a crucial role to determine the instability mechanisms. Moreover,
the unstable modes, which are most likely observed, can be driven by the dependence of surface energy on the surface area.
Low-ordering fibers display the classical axisymmetric mode, since the surface energy decreases by decreasing the surface
area. Decreasing temperature gives rise to the encounter with a local maximum or to monotonic increase of the characteristic
length of the axisymmetric mode. Meanwhile, in the presence of high surface ordering, non-axisymmetric finite wavelength instabilities
emerge, with higher modes growing faster since the surface energy decreases by increasing the surface area. As temperature
decreases, the pitches of the chiral microstructures become smaller. However, this non-axisymmetric instability mechanism
can be regulated by taking account of the surface bending moment, which contains higher order variations in the interface
curvatures. More and more non-axisymmetric modes emerge as temperature decreases, but, at constant temperature, only a finite
number of non-axisymmetric modes are unstable and a single fastest growing mode emerges with lower and higher unstable modes
growing slower. For nematic fibers, the classical fiber-to-droplet transformation is one of several possible instability pathways,
while others include chiral microstructures. The capillary instabilities' growth rate of a thin nematic fiber in a viscous
matrix is suppressed by increasing either the fiber or matrix viscosity, but the estimated droplet sizes after fiber breakup
in axisymmetric instabilities decrease with increasing the matrix viscosity.
Received 15 April 2002 and Received in final form 3 October 2002
RID="a"
ID="a"e-mail: alejandro.rey@mcgill.ca 相似文献
14.
New unstable temperature gradient driven modes in an inhomogeneous tokamak plasma are identified. These modes represent temperature gradient (ion and electron) driven modes destabilized in the short wavelength regions with k( perpendicular )rho(i,e)>1, respectively. The instability occurs due to a specific plasma response that significantly deviates from Boltzmann distribution in the regions k( perpendicular )rho(i,e)>1. 相似文献
15.
Buti B. 《IEEE transactions on plasma science. IEEE Nuclear and Plasma Sciences Society》1976,4(4):292-295
Nonlinear ion-acoustic waves, which in the absence of collisions are moderately stable in the long wave length limit, become modulationally unstable due to presence of collisions. These waves are unstable in the wave number range kmin < k < kmax. 相似文献
16.
Gölles M Darmanyan S Lederer F Onishchukov G Shipulin A Bakonyi Z Lokhnygin V 《Optics letters》2000,25(5):293-295
Modulational instability of continuous waves in transmission systems with semiconductor optical amplifiers and in-line filters was theoretically and experimentally analyzed. Stable and unstable domains were identified. Even in the normal-dispersion region, modulationally unstable domains can exist for an appropriate filter detuning. 相似文献
17.
The modulational instability of ion acoustic waves is studied in the presence of a dc magnetic field, taking the ion temperature into account. It is well known that the instability sets in for wave numbers exceeding 1.47 kD when there is no magnetic field and the ion temperature is negligible. The instability behaviour, however, changes drastically when either the magnetic field is switched on or the ion temperature becomes important or both. In general three different regions emerge wherein the waves becomes modulationally unstable. The relative sizes of these regions change as the magnetic field, the angle of propagation and the ion temperature are varied. 相似文献
18.
《Physics letters. A》2020,384(2):126060
The modulational instability of two-dimensional nonlinear traveling-wave solutions of the Whitham equation in the presence of constant vorticity is considered. It is shown that vorticity has a significant effect on the growth rate of the perturbations and on the range of unstable wavenumbers. Waves with kh greater than a critical value, where k is the wavenumber of the solution and h is the fluid depth, are modulationally unstable. This critical value decreases as the vorticity increases. Additionally, it is found that waves with large enough amplitude are always unstable, regardless of wavelength, fluid depth, and strength of vorticity. Furthermore, these new results are in qualitative agreement with those obtained by considering fully nonlinear solutions of the water-wave equations. 相似文献
19.
The exact nonlinear dispersion relation for circular polarized plane wave propagating along magnetic field in a ferromagnetic system is derived. It is pointed out that the right polarized wave can be modulationally unstable and may evolve into a soliton. 相似文献
20.
A nonlinear Schrödinger equation for ion-acoustic waves in a collision free plasma, consisting of warm ions and hot isothermal electrons is derived using the KBM method. It is found that for finite ion temperature these waves are modulationally unstable only in a range of wave numbers. As the ratio of ion to electron temperature increases, the range of the unstable region decreases and shifts towards small wave numbers. 相似文献