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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

A Hamilton-Jacobi approach to the control of the trapping time of a soliton by an external potential


Authors: G. Kossioris, M. Plexousakis and A. N. Yannacopoulos
Journal: Quart. Appl. Math. 63 (2005), 309-324
MSC (2000): Primary 49L25
Published electronically: February 28, 2005
MathSciNet review: 2150777
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Abstract: The control of the trapping time of a localized solution of the nonlinear Schrödinger equation (NLS) with the use of an external parabolic potential is studied. We reduce the dynamics of the position of the soliton center to those of a controlled linear oscillator and then study the viscosity solution of the associated Hamilton-Jacobi equation. A numerical scheme is proposed for the treatment of the problem.


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Additional Information

G. Kossioris
Affiliation: Department of Mathematics, University of Crete, 71409 Heraklion, Greece ; Institute of Applied and Computational Mathematics, FORTH, 71110 Heraklion, Greece
Email: kosioris@math.uoc.gr

M. Plexousakis
Affiliation: Department of Applied Mathematics, University of Crete, 71409 Heraklion, Greece ; Institute of Applied and Computational Mathematics, FORTH, 71110 Heraklion, Greece
Email: plex@tem.uoc.gr

A. N. Yannacopoulos
Affiliation: Department of Statistics and Actuarial Science, University of the Aegean, 82300 Karlovassi, Samos, Greece
Email: ayannaco@aegean.gr

DOI: http://dx.doi.org/10.1090/S0033-569X-05-00950-0
PII: S 0033-569X(05)00950-0
Received by editor(s): June 1, 2004
Published electronically: February 28, 2005
Article copyright: © Copyright 2005 Brown University



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