As an important model in quantum semiconductor devices, the Schrödinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical op...

The investigation of the exact solutions of nonlinear equations plays an important role in the study of nonlinear physical phenomena. For example, the wave phenomena observed in fluid dynamics, plasma and elastic media are often modelled by the bell shaped sech solutions and the kink shaped tanh traveling wave solutions. The exact solution, if available, of those nonlinear equations facilitates...

We extend the well-known trace formula for Hill's equation to general one-dimensional Schrodinger operators. The new function <J , which we introduce, is used to study absolutely continuous spectrum and inverse problems. In this note we will consider one-dimensional Schrodinger operators d2 (IS) H = -j-1 + V(x) onL2(R;dx)

We elaborate on a new methodology, which starting with an integrable evolution equation in one spatial dimension, constructs forced version of this equation. The forcing consists terms involving quadratic products certain eigenfunctions the associated Lax pair. Remarkably, some these equations arise modelling important physical phenomena. initial value problem can be formulated as Riemann-Hilbe...

we consider a new type of integrable coupled nonlinear schrodinger (cnls)equations proposed by our self [submitted to phys. plasmas (2011)]. the explicitform of soliton solutions are derived using the hirota&apos;s bilinear method.we show that the parameters in the cnls equations only determine the regionsfor the existence of bright and dark soliton solutions. finally, throughthe linear stabili...

Transmission through a potential barrier, and the related issue of particle production from a parametric resonance, are topics of considerable general interest in quantum physics. The authors have developed a rather general bound on quantum transmission probabilities, and recently applied it to bounding the greybody factors of a Schwarzschild black hole. In the current article we take a differe...