We demonstrate a new method to generate second-harmonic Talbot effect through degenerate Cherenkov radiation in one-dimension anomalous-dispersion-like nonlinear photonic crystals. In anomalous-dispersion-like medium, the degenerated nonlinear Cherenkov radiation can be achieved and is parallel to domain walls, of which the intensity is adjusted by the second-order nonlinear coefficient. In thi...

A sol-gel technique under ultrasonic irradiation was applied to synthesize ZrO2/TiO2/ZnOnanocomposites. X-ray diffraction analysis confirmed the successful synthesis of nanocomposites. The strain and crystalline size values of ZrO2/TiO2/ZnO nanocomposites are estimated to be 9.98×10-4 and 17.66 nm, respectively. The linear absorption coefficient of ZrO2/TiO2/ZnO nanocomposites was measure...

Sufficient conditions in terms of the coefficient functions for the oscillation and asymptotic behavior of nonoscillatory solutions of a class of second order nonlinear neutral differential equations have been obtained. The results improve some earlier results.

In this paper, a variable-coefficient Korteweg-de Vries (vcKdV) equation which was proposed to describe the propagation of weakly nonlinear waves in water of variable depth is investigated in detail. Firstly, the Lie point symmetries and some group invariant solutions of this equation are presented. Furthermore, the integrability property of this variable-coefficient equation is studied followi...