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...

We examine the use of orthogonal spline collocation for the semi-discretization of the cubic Schr odinger equation and the two-dimensional parabolic equation of Tappert. In each case, an optimal order L 2 estimate of the error in the semidiscrete approximation is derived. For the cubic Schr odinger equation, we present the results of numerical experiments in which the integration in time is p...

This paper is devoted to the asymptotic properties of the Nonlinear Schrr odinger equation in the defocusing case. We recover dispersion rates by the mean of time-dependent rescalings in the power law case and prove a new result in the case of the logarithmic Nonlinear Schrr odinger equation. The rescaled equation is then used to obtain an asymptotic result of nonlinear stability, which is the ...

We examine the use of orthogonal spline collocation for the semi-discretization of the cubic Schrr odinger equation and the two-dimensional parabolic equation of Tappert. In each case, an optimal order L 2 estimate of the error in the semidiscrete approximation is derived. For the cubic Schrr odinger equation, we present the results of numerical experiments in which the integration in time is p...

The one-dimensional matrix Schrr odinger equation is considered when the matrix potential is selfadjoint and satisses certain general restrictions. The small-energy asymptotics of the scattering solutions and scattering coeecients are derived. The continuity of the scattering coeecients is established. The unique solvability of the corresponding matrix Marchenko integral equations is proved. Sh...

In this paper, we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators and efficient integration of the Schr¨odinger equation. The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant lit...

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.

A detailed review is given of the semiclassical approximation to quantum gravity in the canonical framework. This includes in particular the derivation of the functional Schrodinger equation and a discussion of semiclassical time as well as the derivation of quantum gravitational correction terms to the Schrodinger equation. These terms are used to calculate energy shifts for elds in De Sitte...

The methods of stochastic control theory are proposed in the context of charged-particle beam dynamics. The stochastic dynamics that is introduced here is invariant for time reversal and can be easily recast in the form of a Schrr odinger-like equation where Planck's constant is replaced by the beam emittance. It changes a bilinear control problem for Schrr odinger equation in a linear control ...