Multiple solutions of discrete Schrödinger equations with growing potentials

Time decay for solutions of Schrödinger equations with rough and time - dependent potentials

In this paper we establish dispersive estimates for solutions to the linear Schrödinger equation in three dimension 1 i ∂ t ψ − △ψ + V ψ = 0, ψ(s) = f (0.1) where V (t, x) is a time-dependent potential that satisfies the conditions sup t V (t, ·)

2 00 1 Time decay for solutions of Schrödinger equations with rough and time - dependent potentials

In this paper we establish dispersive estimates for solutions to the linear Schrödinger equation in three dimension 1 i ∂ t ψ − △ψ + V ψ = 0, ψ(s) = f (0.1) where V (t, x) is a time-dependent potential that satisfies the conditions sup t V (t, ·)

Controllability properties of discrete-spectrum Schrödinger equations

We state an approximate controllability result for the bilinear Schrödinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. This result applies both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. In addition we get some controllability properties for the density matrix. Finally we show, by me...

Soliton Solutions for Quasilinear Schrödinger Equations

Discrete nonlinear Schrödinger equations with arbitrarily high-order nonlinearities.

A class of discrete nonlinear Schrödinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrödinger equation and the Ablowitz-Ladik equation. As a common property, these equations possess three kinds of exact analytical sta...