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.

Grey screening-photovoltaic soliton-induced waveguides

This paper shows that waveguides induced by grey screening-photovoltaic solitons are always single mode for all intensity ratios, which are the ratio between the peak intensity of the soliton and the dark irradiance. It finds that the confined energy near the centre of the grey soliton and the propagation constant of the guided mode increase monotonically with increasing intensity ratio. On the other hand, when the soliton greyness increases, the confined energy near the centre of the grey soliton and the propagation constant of the guided mode reduce monotonically. When the bulk photovoltaic effect is neglected for short circuits, these waveguides become waveguides induced by grey screening solitons. When the external bias field is absent, these waveguides become waveguides induced by grey photovoltaic solitons.

Soliton-induced waveguides in photorefractive photovoltaic materials

Waveguides induced by one-dimensional spatial photovoltaic solitons are investigated in both self-defocusing-type and self-focusing-type photorefractive photovoltaic materials. The number of possible guided modes in a waveguide induced by a bright photovoltaic soliton is obtained using numerical techniques. This number of guided modes increases monotonically with increasing intensity ratio, which is the ratio between the peak intensity of the soliton and the sum of the background illumination and the dark irradiance. On the other hand, waveguides induced by dark photovoltaic solitons are always single mode for all intensity ratios, and the higher the intensity ratio, the more confined is the optical energy near the centre of the dark photovoltaic soliton. Relevant examples are provided where photorefractive photovoltaic materials are of self-defocusing and self-focusing types. The properties of soliton-induced waveguides in both self-defocusing-type and self-focusing-type materials are also discussed.