This paper discusses the inhomogeneous nonlinear Schrödinger equation with critical exponent. By constructing a variational problem and the so-called invariant manifolds of the evolution flow, we derive a sharp criterion for blowup and global existence of the solutions.

As nowadays semiconductor devices are characterized by active lengths on the nanometer scale, it is important to use models including fully the quantum mechanical effects. In this paper we focus on the Wigner equation, a convenient reformulation of the Schrödinger equation in terms of a...

The system of coupled nonlinear Schrödinger’s equations (CNLSE) is considered and the physical meaning of the coupling terms is identified. The attention is focused on the case of real-valued parameter of linear cross-diffusion. A new analytical solution for the coupled case is found and used...

The electron flow through quantum waveguides is modeled by the time-dependent Schrödinger equation with absorbing boundary conditions, which are realized by a negative imaginary potential. The Schrödinger equation is discretized by a time-splitting spectral method, and the quantum waveguides...

We investigate the propagation of ultrashort solitons in fiber-optic systems in the presence of the soliton self-frequency shift effect. It is demonstrated that both the self-frequency shift and the background instability can be effectively controlled using spectral filters of moderate strength...

An expert system for the numerical integration of the phase shift problem of the one-dimensional Schrödinger equation is proposed in this paper.

We consider the two-dimensional, time-dependent Schrödinger equation discretized with the Crank–Nicolson finite difference scheme. For this difference equation we derive discrete transparent boundary conditions (DTBCs) in order to get highly accurate solutions for open boundary problems. We...