Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping

Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping

We study the dynamical behavior of solutions of an n-dimensional nonlinear Schrödinger equation with potential and linear derivative terms under the presence of phenomenological damping. This equation is a general version of the dissipative Gross-Pitaevskii equation including terms with first-order...

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Main Authors: Renato Colucci, Gerardo R. Chacón, Andrés Vargas
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2013/874196
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spelling doaj-b9d68f8a620b4c888d1e65c777dffbe22020-11-24T23:01:59ZengHindawi LimitedInternational Journal of Differential Equations1687-96431687-96512013-01-01201310.1155/2013/874196874196Dynamics of a Gross-Pitaevskii Equation with Phenomenological DampingRenato Colucci0Gerardo R. Chacón1Andrés Vargas2Departamento de Matemáticas, Pontificia Universidad Javeriana, Carrera 7 No. 40-62, Bogotá, ColombiaDepartamento de Matemáticas, Pontificia Universidad Javeriana, Carrera 7 No. 40-62, Bogotá, ColombiaDepartamento de Matemáticas, Pontificia Universidad Javeriana, Carrera 7 No. 40-62, Bogotá, ColombiaWe study the dynamical behavior of solutions of an n-dimensional nonlinear Schrödinger equation with potential and linear derivative terms under the presence of phenomenological damping. This equation is a general version of the dissipative Gross-Pitaevskii equation including terms with first-order derivatives in the spatial coordinates which allow for rotational contributions. We obtain conditions for the existence of a global attractor and find bounds for its dimension.http://dx.doi.org/10.1155/2013/874196
collection DOAJ
language English
format Article
sources DOAJ
author Renato Colucci
Gerardo R. Chacón
Andrés Vargas
spellingShingle Renato Colucci
Gerardo R. Chacón
Andrés Vargas
Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping
International Journal of Differential Equations
author_facet Renato Colucci
Gerardo R. Chacón
Andrés Vargas
author_sort Renato Colucci
title Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping
title_short Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping
title_full Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping
title_fullStr Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping
title_full_unstemmed Dynamics of a Gross-Pitaevskii Equation with Phenomenological Damping
title_sort dynamics of a gross-pitaevskii equation with phenomenological damping
publisher Hindawi Limited
series International Journal of Differential Equations
issn 1687-9643
1687-9651
publishDate 2013-01-01
description We study the dynamical behavior of solutions of an n-dimensional nonlinear Schrödinger equation with potential and linear derivative terms under the presence of phenomenological damping. This equation is a general version of the dissipative Gross-Pitaevskii equation including terms with first-order derivatives in the spatial coordinates which allow for rotational contributions. We obtain conditions for the existence of a global attractor and find bounds for its dimension.
url http://dx.doi.org/10.1155/2013/874196
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AT gerardorchacon dynamicsofagrosspitaevskiiequationwithphenomenologicaldamping
AT andresvargas dynamicsofagrosspitaevskiiequationwithphenomenologicaldamping
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