in this paper, we establish the existence and uniqueness result of the linear schrodinger equation with marchaud fractional derivative in colombeau generalized algebra. the purpose of introducing marchaud fractional derivative is regularizing it in colombeau sense.

The one-dimensional Schrodinger equation and two of its generalizations are considered, as they arise in quantum mechanics, wave propagation in a nonhomogeneous medium, and wave propagation in a nonconservative medium where energy may be absorbed or generated. Generically, the zero-energy transmission coe cient vanishes when the potential is nontrivial, but in the exceptional case this coe cie...

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'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...

Two disordered models are considered: spherical model and non-interacting electron gas on lattice. The supersymmetry representation for correlation functions of these models is obtained. Using this representation the conngura-tional averaging can be performed before thermodynamical one and the problem of calculation of conngurationally averaged correlation functions of disordered spherical mode...

We study Schr odinger semigroups in the scale of Sobolev spaces and show that for Kato class potentials the range of such semigroups in Lp has exactly two more derivatives than the potential this proves a conjecture of B Simon We show that eigenfunctions of Schr odinger operators are generically smoother by exactly two derviatives in given Sobolev spaces than their potentials We give applicatio...

In this paper we reconsider in the light of the Nelson stochastic mechanics the idea originally proposed by Bohm and Vigier that arbitrary solutions of the evolution equation for the probabil ity densities always relax in time toward the quantum mechanical density j j derived from the Schr odinger equation The analysis of a few general propositions and of some physical examples show that the ch...

The one-dimensional Schrodinger equation is considered when the potential and its rst moment are absolutely integrable. The potential is uniquely constructed in terms of the scattering data consisting of the re ection coe cient from the right (left) and the knowledge of the potential on the right (left) half line of the real axis. Hence, neither the bound state energies nor the bound state nor...

A method is proposed for finding exact solutions of the nonlinear Schr~dinger equation. It uses an ansatz in which the real and imaginary parts of the unknown function are connected by a linear relation with coefficients that depend only on the time. The method consists of constructing a system of ordinary differential equations whose solutions determine solutions of the nonlinear Schr~dinger e...

Transverse{tracefree (TT{) tensors on (R 3 ; g ab), with g ab an asymptotically at metric of fast decay at innnity, are studied. When the source tensor from which these TT tensors are constructed has fast fall{oo at innnity, TT tensors allow a multipole{type expansion. When g ab has no conformal Killing vectors (CKV's) it is proven that any nite but otherwise arbitrary set of moments can be rea...

We study the graded derivation-based noncommutative diierential geometry of the Z 2-graded algebra M (njm) of complex (n + m) (n + m)-matrices with the \usual block matrix grading" (for n 6 = m). Beside the (innnite-dimensional) algebra of graded forms the graded Cartan calculus, graded symplectic structure, graded vector bundles, graded connections and curvature are introduced and investigated...