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.

One-dimensional modulation instability of broad optical beams in biased photorefractive-photovoltaic crystals under steady-state conditions

We present a comprehensive study of the one-dimensional modulation instability of broad optical beams in biased photo refractive-photovoltaic crystals under steady-state conditions. We obtain the one-dimensional modulation instability growth rate by globally treating the space-charge field and by considering distinction between values of Eo in nonlocal effects and local effects in the space-charge field, where Eo is the field constant correlated with terms in the space-charge field, which depends on the external bias field, the bulk photovoltaic effect, and the ratio of the optical beam's intensity to that of the dark irradiance. The one-dimensional modulation instability growth rate in local effects can be determined from that in nonlocal effects. When the bulk photovoltaic effect is neglectable, irrespective of distinction between values of Eo in nonlocal effects and local effects in the space-charge field, the one-dimensional modulation instability growth rates in nonlocal effects and local effects are those of broad optical beams studied previously in biased photorefractive-nonphotovoltaic crystals. When the external bias field is absent, the one-dimensional modulation instability growth rates in nonlocal effects and local effects predict those of broad optical beams in open- and closed-circuit photorefractive-photovoltaic crystals. (c) 2004 Elsevier B.V. All rights reserved.

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.

IMPROVEMENT OF STRUCTURAL INSTABILITY OF THE ION-SENSITIVE FIELD-EFFECT TRANSISTOR (ISFET)

Three causes involved in the instability of the ISFET are proposed in this study. First, it is ascertained that hydroxyl group resident at the surface of the Si3N4 film or in the electrolyte solution is most active and subject to gain or loss of electrons. This is one of the main causes for ISFET structural instability. Secondly, the stability of the pH-sensitive FET varies with deposition conditions in the fabrication process of the ISFET. This proves to be another cause of ISFET instability. Thirdly, the pH of the measured solution varies with the measuring process and time, contributing to the instability, but is not a cause of the instability of the pH-ISFET itself. We utilized the technique of readjusting and controlling the ratio of hydroxyl groups to amine groups to enhance the stability of the ISFET. Our techniques to improve stability characteristics proved to be effective in practice.