Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2014-08-26Online Publication Date
2014-08-26Print Publication Date
2014-12Permanent link to this record
http://hdl.handle.net/10754/563715
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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.Citation
Hadj Selem, F., Hajaiej, H., Markowich, P. A., & Trabelsi, S. (2014). Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation. Milan Journal of Mathematics, 82(2), 273–295. doi:10.1007/s00032-014-0227-5Sponsors
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.Publisher
Springer NatureJournal
Milan Journal of Mathematicsae974a485f413a2113503eed53cd6c53
10.1007/s00032-014-0227-5