Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Online Publication Date2014-08-26
Print Publication Date2014-12
Permanent link to this recordhttp://hdl.handle.net/10754/563715
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AbstractThis 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.
CitationHadj 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/s00032-014-0227-5
SponsorsH. 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.
JournalMilan Journal of Mathematics