Displaying similar documents to “The continuous Coupled Cluster formulation for the electronic Schrödinger equation”

Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields

Huirong Pi, Chunhua Wang (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we are concerned with the existence of multi-bump solutions for a nonlinear Schrödinger equations with electromagnetic fields. We prove under some suitable conditions that for any positive integer , there exists () > 0 such that, for 0 <  < (), the problem has an -bump complex-valued solution. As a result, when  → 0, the equation has more and more multi-bump complex-valued solutions.

Controllability of Schrödinger equation with a nonlocal term

Mariano De Leo, Constanza Sánchez Fernández de la Vega, Diego Rial (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper is concerned with the internal distributed control problem for the 1D Schrödinger equation,   () = − +() +() , that arises in quantum semiconductor models. Here () is a non local Hartree–type nonlinearity stemming from the coupling with the 1D Poisson equation, and () is a regular function with linear growth at infinity, including constant electric fields. By means of both the Hilbert Uniqueness Method and the contraction mapping theorem it is...

A posteriori error analysis for the Crank-Nicolson method for linear Schrödinger equations

Irene Kyza (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We prove error estimates of optimal order for linear Schrödinger-type equations in the ( )- and the ( )-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis in [ 75 (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ( ...

Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity

Sorin Micu, Ionel Rovenţa (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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This article considers the linear 1-d Schrödinger equation in (0) perturbed by a vanishing viscosity term depending on a small parameter  > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls as goes to zero. It is shown that, for any time sufficiently large but independent of and for each initial datum in ...

Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity

Sorin Micu, Ionel Rovenţa (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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This article considers the linear 1-d Schrödinger equation in (0) perturbed by a vanishing viscosity term depending on a small parameter  > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls as goes to zero. It is shown that, for any time sufficiently large but independent of and for each initial datum in ...

error analysis for the Crank-Nicolson method for linear Schrödinger equations

Irene Kyza (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We prove error estimates of optimal order for linear Schrödinger-type equations in the ( )- and the ( )-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis in [ (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ...

High-frequency limit of the Maxwell-Landau-Lifshitz equations in the diffractive optics regime

LU Yong (2012)

ESAIM: Proceedings

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We study the Maxwell-Landau-Lifshitz system for highly oscillating initial data, with characteristic frequencies (1  ) and amplitude (1), over long time intervals (1  ), in the limit  → 0. We show that a nonlinear Schrödinger equation gives a good approximation for the envelope of the solution in the time interval under consideration. This extends previous results of Colin and Lannes [1]. This text is a short version of the article [5].

On Numerical Solution of the Gardner–Ostrovsky Equation

M. A. Obregon, Y. A. Stepanyants (2012)

Mathematical Modelling of Natural Phenomena

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A simple explicit numerical scheme is proposed for the solution of the Gardner–Ostrovsky equation ( + + + + ) = which is also known as the extended rotation-modified Korteweg–de Vries (KdV) equation. This equation is used for the description of internal oceanic waves affected by Earth’ rotation. Particular...