the paper is devoted to the study of brenstien polynomials and development of some new operational matrices of fractional order integrations and derivatives. the operational matrices are used to convert fractional order differential equations to systems of algebraic equations. a simple scheme yielding accurate approximate solutions of the couple systems for fractional differential equations is ...

Asymptotic quantum transport models of a two-dimensional electron gas are presented. The starting point is a singular perturbation of the threedimensional Schrödinger-Poisson system. The small parameter ε is the scaled width of the electron gas and appears as the lengthscale on which a one dimensional confining potential varies. The rigorous ε→ 0 limit is performed by projecting the three dimen...

In Chen and Kulik, 2009 , a method of renormalization was proposed for constructing some more physically realistic random potentials in a Poisson cloud. This paper is devoted to the detailed analysis of the asymptotic behavior of the annealed negative exponential moments for the Brownian motion in a renormalized Poisson potential. The main results of the paper are applied to studying the Lifshi...

All Lie bialgebra structures for the (1+ 1)-dimensional centrally extended Schrödinger algebra are explicitly derived and proved to be of the coboundary type. Therefore, since all of them come from a classical r-matrix, the complete family of Schrödinger Poisson–Lie groups can be deduced by means of the Sklyanin bracket. All possible embeddings of the harmonic oscillator, extended Galilei and g...

This paper is motivated by the study of a version of the so-called Schrödinger-Poisson-Slater problem: −∆u+ ωu+ λ „

The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...

Abstract We deal with multiplicity of solutions to the following Schrödinger-Poisson-type system in this article: Δ H u −</m:mo...

We prove Strichartz estimates with fractional loss of derivatives for the Schrödinger equation on any riemannian compact manifold. As a consequence we infer global existence results for the Cauchy problem of nonlinear Schrödinger equations on surfaces in the case of defocusing polynomial nonlinearities, and on three–manifolds in the case of quadratic nonlinearities. We also discuss the optimali...