Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity

In this Letter we deal with a nonlinear Schrodinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Here we show that the chaotic perturbation is more effective in destroying the soliton behavior, when compared with random or nonperiodic perturbation. For a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein condensates and their collective excitations and transport. (C) 2010 Elsevier B.V. All rights reserved.

Dirac equation in noncommutative space for hydrogen atom

We consider the energy levels of a hydrogen-like atom in the framework of theta-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S(1/2), 2P(1/2) and 2P(3/2) is lifted completely, such that new transition channels are allowed. (C) 2009 Elsevier B.V. All rights reserved.

A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

Formation of beta-nickel hydroxide plate-like structures under mild conditions and their optical properties

Nanostructural beta-nickel hydroxide (beta-Ni(OH)(2)) plates were prepared using the microwave hydrothermal (MH) method at a low temperature and short reaction times. An ammonia solution was employed as the coordinating agent, which reacts with [Ni(H(2)O)(6)](2+) to control the growth of beta-Ni(OH)(2) nuclei. A trigonal beta-Ni(OH)(2) single phase was observed by X-ray diffraction (XRD) analyses, and the crystal cell was constructed with structural parameters and atomic coordinates obtained from Rietveld refinement. Field emission scanning electron microscopy (FE-SEM) images revealed that the samples consisted of hexagonal-shaped nanoplates with a different particle size distribution. Broad absorption bands assigned as transitions of Ni(2+) in oxygen octahedral sites were revealed by UV-vis spectra. Photoluminescence (PL) properties observed with a maximum peak centered in the blue-green region were attributed to different defects, which were produced during the nucleation process. We present a growth process scheme of the beta-Ni(OH)(2) nanoplates. (C) 2011 Elsevier Inc. All rights reserved.

A multivariate ultrastructural errors-in-variables model with equation error

This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors Sufficient conditions for attaining consistent estimators for model parameters are presented Asymptotic distributions for the line regression estimators are derived Applications to the elliptical class of distributions with two error assumptions are presented The model generalizes previous results aimed at univariate scenarios (C) 2010 Elsevier Inc All rights reserved

A DISCRETIZATION SCHEME FOR AN ONE-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH DELAY AND ITS DYNAMICS

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.

On the Hamilton-Jacobi equation in the framework of generalized functions

In this work we study, in the framework of Colombeau`s generalized functions, the Hamilton-Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions. (C) 2011 Elsevier Inc. All rights reserved.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.