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We derive high-order corrections to a modulation theory for the propagation of internal gravity waves in a density-stratified fluid with coupling to the mean flow. The methodology we use allows for strong modulations of wavenumber and mean flow, extending previous approaches developed for the quasi-monochromatic regime. The wave mean flow modulation equations consist of a system of nonlinear conservation laws that may be hyperbolic, elliptic or of mixed type. We investigate the regularizing properties of the asymptotic correction terms in the case when the system becomes unstable and ill-posed due to a change of type (loss of hyperbolicity). A linear analysis reveals that the regularization by the added correction terms does so by introducing a short-wave cut-off of the unstable wavenumbers. We perform various numerical experiments that confirm the regularizing properties of the correction terms, and show that the growth of unstable modes is tempered by nonlinearity. We also find an excellent agreement between the solution of the corrected modulation system and the modulation variables extracted from the numerical solution of the nonlinear Boussinesq equations. 相似文献
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Saroj K Majumdar 《Pramana》1984,23(6):785-801
The nonlinear distribution function of Allis, generalised to include the transverse electromagnetic waves in a plasma, is
used to set up the coupled wave equations for the longitudinal and the transverse modes. These are solved, keeping terms up
to the cubic order of nonlinearity, by using the method of multiple scales. The equations of wave modulation are derived,
which are solved to discuss the nature of the modulational instability and solitary wave propagation. It is found that the
solutions so obtained satisfy conditions which are very similar to the well known Lighthill criterion for stability, appropriately
modified due to the coupling of the two modes. The role of the average constant current due to any flow of the resonant and
trapped electrons in determining the stability, is also discussed. 相似文献
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The dynamic behaviors of nonlinear periodic waveguides with a finite material response time have been investigated by numerically solving both the coupled-mode equations and Debye relaxation equation. When the response time of the nonlinearity is more than the transit time through the grating, a modulational instability is sufficiently suppressed and one can obtain optical bistability. Unlike a nonlinear Fabry-Perot resonator or ring resonators, overshoot in the transmission never takes place in the case of zero detuning. However, a relaxation (or damped) oscillation always takes place in the presence of detuning. It is also found that the switch-on time depends on the material response time and the switch-off time is almost independent of it. 相似文献
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We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-onedimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our results reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable. 相似文献
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We investigate modulational instability (MI) of a coupled two-component Bose-Einstein condensates in a rotating ring trap. The excitation spectrum and the MI condition of the system are presented analytically. We find that the coupling between the two components strongly modifies the MI condition, and the MI condition is phase-dependent. Furthermore, we discuss the effect of MI on both density excitation and spin excitation. If the inter- and intra-component interaction strengths are all equal, the MI causes density excitation but not spin excitation, and if the inter- and intra-component interaction strengths are different, the MI causes both density excitation and spin excitation. Our results provide a promising approach for controlling the stability and excitation of a rotating two-component Bose-Einstein condensates by modulating its coupling strength and interaction strength. 相似文献
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WANG Yue-Yue DAI Chao-Qing ZHANG Jie-Fang 《理论物理通讯》2009,51(1):81-89
In this paper, exact and numerical solutions are calculated for discrete complex Ginzburg-Landau equation with initial condition by considering the modified Adomian decomposition method (mADM), which is an efficient method and does not need linearization, weak nonlinearity assumptions or perturbation theory. The numerical solutions are also compared with their corresponding analytical solutions. It is shown that a very good approximation is achieved with the analytical solutions. Finally, the modulational instability is investigated and the corresponding condition is given. 相似文献
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Modulational instability of incoherently coupled beams in azobenzene-containing polymer with photoisomerization nonlinearity
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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. 相似文献
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Using the standard reductive perturbation technique,a nonlinear Schroedinger equation is derived to study the modulational instability of finite-amplitude ion-acoustic waves in a non-magnetized warm plasma.It is found that the inclusion of ion temperature in the equation modifies the nature of the ion-acoustic wave stability and the soliton stuctures.The effects of ion plasma temperature on the modulational stability and ion-acoustic wave properties are inestigated in detail. 相似文献