instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities

This paper discusses the Klein–Gordon–Zakharov system with different-degree nonlinearities in two and three space dimensions. Firstly, we prove the existence of standing wave with ground state by applying an intricate variational argument. Next, by introducing an auxiliary functional and an equivalent minimization problem, we obtain two invariant manifolds under the solution flow generated by the Cauchy problem to the aforementioned Klein–Gordon–Zakharov system. Furthermore, by constructing a type of constrained variational problem, utilizing the above two invariant manifolds as well as applying potential well argument and concavity method, we derive a sharp threshold for global existence and blowup. Then, combining the above results, we obtain two conclusions of how small the initial data are for the solution to exist globally by using dilation transformation. Finally, we prove a modified instability of standing wave to the system under study.

measuring acoustic wave transit time in furnace based on active acoustic source signal

Accurate measurement of transit time for acoustic wave between two sensors installed on two sides of a furnace is a key to implementing the temperature field measurement technique based on acoustical method. A new method for measuring transit time of acoustic wave based on active acoustic source signal is proposed in this paper, which includes the followings: the time when the acoustic source signal arrives at the two sensors is measured first; then, the difference of two arriving time arguments is computed, thereby we get the transit time of the acoustic wave between two sensors installed on the two sides of the furnace. Avoiding the restriction on acoustic source signal and background noise, the new method can get the transit time of acoustic wave with higher precision and stronger ability of resisting noise interference.

Two-dimensional numerical simulations of shock waves in micro convergent-divergent nozzles

The steady two-dimensional Navier-Stokes equations with the slip wall boundary conditions were used to simulate the supersonic flow in micro convergent-divergent nozzles. It is observed that shock waves can take place inside or outside of the micronozzles under the earth environment. For the over-expanded flows, there is a boundary layer separation point, downstream of which a wave interface separates the viscous boundary layer with back air flow and the inviscid core flow. The oblique shock wave is followed by the bow shock and shock diamond. The viscous boundary layer thickness relative to the whole nozzle width on the exit plane is increased but attains the maximum value around of 0.5 and oscillates against this value with the continuous increasing of the nozzle upstream pressures. The viscous effect either changes the normal shock waves outside of the nozzle for the inviscid flow to the oblique shock waves inside the nozzle, or transfers the expansion jet flow without shock waves for the inviscid flow to the oblique shock waves outside of the nozzle. 

Four-wave mixing self-stability based on photonic crystal fiber and its applications on erbium-doped fiber lasers

The analytic solutions of coupled-mode equations of four-wave mixings (FWMs) are achieved by means of the undepleted approximation and the perturbation method. The self-stability mechanism of the FWM processes is theoretically proved and is applicable to design a new kind of triple-wavelength erbium-doped fiber lasers. The proposed fiber lasers with excellent stability and uniformity are demonstrated by using a flat-near-zero-dispersion high-nonlinear photonic-crystal-fiber. The significant excellence is analyzed in theory and is proved in experiment. Our fiber lasers can stably lase three waves with the power ripple of less than 0.4 dB. (c) 2005 Elsevier B.V. All rights reserved.

Interactions of three dual-dressing effects of four-wave mixing in a five-level atomic system

We study the four-wave mixing (FWM) in an opening five-level system with two dressing fields. There are three kinds of doubly dressing mechanisms (parallel cascade, sequential cascade, and nested cascade) in the system for doubly dressed four-wave mixing. These mechanisms reflect different correlations between two dressing fields and different effects of two dressing fields to the FWM. Investigation of these mechanisms is helpful to understand the generated high-order nonlinear optical signal dressed by multi-fields.

Observation of quantum beat in Rb by parametric four-wave mixing

Two coupled parametric four-wave-mixing processed in Rb atoms are studied using perturbation theory, which reveals clear evidence of the appearance of quantum beat at 608 cm(-1), corresponding to the energy difference of the 7s - 5d states of Rb atoms, in the parametric four-wave-mixing signals. A pump-probe technique is utilized to observe the quantum beat. Time-varying characteristics of the quantum beat are investigated using time-dependent Fourier transform. The results show that the time-varying characteristics of the quantum beat potential tool for monitoring the dissociation of molecules.

Modulation instability of quasi-plane-wave optical beams in biased photorefractive-photovoltaic crystals

We investigate the modulation instability of quasi-plane-wave optical beams in biased photorefractive-photovoltaic crystals by globally treating the space-charge field. The modulation instability growth rate is obtained, which depends on the external bias field, on the bulk photovoltaic effect, and on the ratio of the optical beam's intensity to that of the dark irradiance. Our analysis indicates that this modulation instability growth rate is identical to the modulation instability growth rate studied previously in biased photorefractive-nonphotovoltaic crystals when the bulk photovoltaic effect is negligible for shorted circuits, and predicts the modulation instability growth rate in open- and closed-circuit photorefractive-photovoltaic crystals when the external bias field is absent.

Six-wave mixing phase-dispersion by optical heterodyne detection in dressed reverse N-type four-level system

We have investigated the dressed effects of non-degenerate four-wave mixing (NDFWM) and demonstrated a phase-sensitive method of studying the fifth-order nonlinear susceptibility due to atomic coherence in RN-type four-level system. In the presence of a strong coupling field, NDFWM spectrum exhibits Autler-Townes splitting, accompanied by either suppression or enhancement of the NDFWM signal, which is directly related to the competition between the absorption and dispersion contributions. The heterodyne-detected nonlinear absorption and dispersion of six-wave mixing signal in the RN-type system show that the hybrid radiation-matter detuning damping oscillation is in the THz range and can be controlled and modified through the colour-locked correlation of twin noisy fields.

Dressed multi-wave mixing in a V-type four-level atomic system

The dressed four- and six-wave mixings in a V-type four-level system are considered. Under two different dressed conditions, two- and three-photon resonant Autler-Townes splittings, accompanied by enhancement and suppression of wave mixing signal, are obtained analytically. Meanwhile, an electromagnetic induced transparency of multi-wave mixing is presented, which shows multiple peaks and asymmetric effects caused by one-photon, two-photon and three-photon resonances, separately. The slow light propagation multiple region of multi-wave mixing signal is also obtained.