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

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• 作者：Fouad Hadj Selem (1)
  Hichem Hajaiej (2)
  Peter A. Markowich (3)
  Saber Trabelsi (3)
  
• 关键词：35J60 ; 37J10 ; 35Q55 ; 35P30 ; Constrained minimization problem ; nonlinear Schr?dinger equation ; eigenvalue problem
• 刊名：Milan Journal of Mathematics
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：82
• 期：2
• 页码：273-295
• 全文大小：1,413 KB
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• 作者单位：Fouad Hadj Selem (1)
  Hichem Hajaiej (2)
  Peter A. Markowich (3)
  Saber Trabelsi (3)
  
  1. French Atomic Energy Commission, Neurospin, Saclay, France
  2. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia
  3. Division of Mathematics & Computer Science & Engineering, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia
  
• ISSN：1424-9294

文摘

This paper is concerned with the mathematical analysis of a masssubcritical nonlinear Schr?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.