Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation

Fouad Hadj Selem; Hichem Hajaiej; Peter A. Markowich; Saber Trabelsi

doi:10.1007/s00032-014-0227-5

Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation

Fouad Hadj Selem, Hichem Hajaiej, Peter A. Markowich, Saber Trabelsi

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

This paper is concerned with the mathematical analysis of a masssubcritical nonlinear Schrödinger equation arising from fiber optic applications. We show the existence and symmetry of minimizers of the associated constrained variational problem. We also prove the orbital stability of such solutions referred to as standing waves and characterize the associated orbit. In the last section, we illustrate our results with few numerical simulations. © 2014 Springer Basel.

Original language	English (US)
Pages (from-to)	273-295
Number of pages	23
Journal	Milan Journal of Mathematics
Volume	82
Issue number	2
DOIs	https://doi.org/10.1007/s00032-014-0227-5
State	Published - Aug 26 2014

ASJC Scopus subject areas

General Mathematics

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title = "Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation",

abstract = "This paper is concerned with the mathematical analysis of a masssubcritical nonlinear Schr{\"o}dinger equation arising from fiber optic applications. We show the existence and symmetry of minimizers of the associated constrained variational problem. We also prove the orbital stability of such solutions referred to as standing waves and characterize the associated orbit. In the last section, we illustrate our results with few numerical simulations. {\textcopyright} 2014 Springer Basel.",

author = "{Hadj Selem}, Fouad and Hichem Hajaiej and Markowich, {Peter A.} and Saber Trabelsi",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: H. Hajaiej would like to thank NPST for its support through the research project number MA1716. The research of P. A. Markowich and S. Trabelsi reported in this publication was supported by the King Abdullah University of Science and Technology.",

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T1 - Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation

AU - Hadj Selem, Fouad

AU - Hajaiej, Hichem

AU - Markowich, Peter A.

AU - Trabelsi, Saber

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: H. Hajaiej would like to thank NPST for its support through the research project number MA1716. The research of P. A. Markowich and S. Trabelsi reported in this publication was supported by the King Abdullah University of Science and Technology.

PY - 2014/8/26

Y1 - 2014/8/26

N2 - This paper is concerned with the mathematical analysis of a masssubcritical nonlinear Schrödinger equation arising from fiber optic applications. We show the existence and symmetry of minimizers of the associated constrained variational problem. We also prove the orbital stability of such solutions referred to as standing waves and characterize the associated orbit. In the last section, we illustrate our results with few numerical simulations. © 2014 Springer Basel.

AB - This paper is concerned with the mathematical analysis of a masssubcritical nonlinear Schrödinger equation arising from fiber optic applications. We show the existence and symmetry of minimizers of the associated constrained variational problem. We also prove the orbital stability of such solutions referred to as standing waves and characterize the associated orbit. In the last section, we illustrate our results with few numerical simulations. © 2014 Springer Basel.

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UR - http://link.springer.com/10.1007/s00032-014-0227-5

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DO - 10.1007/s00032-014-0227-5

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JO - Milan Journal of Mathematics

JF - Milan Journal of Mathematics

IS - 2

ER -

Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation

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