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

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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.

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Authors and Affiliations

  1. French Atomic Energy Commission, Neurospin, Saclay, France

    Fouad Hadj Selem

  2. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    Hichem Hajaiej

  3. Division of Mathematics & Computer Science & Engineering, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia

    Peter A. Markowich & Saber Trabelsi

Authors
  1. Fouad Hadj Selem
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  2. Hichem Hajaiej
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  3. Peter A. Markowich
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  4. Saber Trabelsi
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Correspondence to Peter A. Markowich.

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Hadj Selem, F., Hajaiej, H., Markowich, P.A. et al. Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation. Milan J. Math. 82, 273–295 (2014). https://doi.org/10.1007/s00032-014-0227-5

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  • DOI: https://doi.org/10.1007/s00032-014-0227-5

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