Nonlinearization and waves in bounded media: old wine in a new bottle

We consider problems such as a standing wave in a closed straight tube, a self-sustained oscillation, damped resonance, evolution of resonance and resonance between concentric spheres. These nonlinear problems, and other similar ones, have been solved by a variety of techniques when it is seen that linear theory fails. The unifying approach given here is to initially set up the appropriate linear difference equation, where the difference is the linear travel time. When the linear travel time is replaced by a corrected nonlinear travel time, the nonlinear difference equation yields the required solution

Time-dependent transport properties in quantum well with thin inserted layer

We investigate the time-dependent transport properties of quantum well on the situation of nonlinear bias, where a thin potential well layer is inserted in the main quantum well. In our calculations, we consider the effects from all kinds of phonon interactions in the device. We find that the charge redistribution and electron motion in the whole structure play an important effect on the final current-voltage (I-V) curve. We also find an evident current hysteresis region and current high-frequency oscillation with time in this particular region. The results show that the inserted potential well layer can make the current hysteresis width narrower than that in the single quantum well structure, and it also damps the current oscillation. Due to the existence of the inserted layer, the plateau structure of I-V curve found in the single quantum well disappears. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005