Variational approach to dynamics of bright solitons in lossy optical fibers.
Mahmood, M. F., Brooks, S. (2003)
International Journal of Mathematics and Mathematical Sciences
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Mahmood, M. F., Brooks, S. (2003)
International Journal of Mathematics and Mathematical Sciences
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Kumar, Arun (2005)
International Journal of Mathematics and Mathematical Sciences
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Kingsep, A. (1999)
Discrete Dynamics in Nature and Society
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Jürg Fröhlich, Enno Lenzmann (2003-2004)
Séminaire Équations aux dérivées partielles
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We discuss the Hartree equation arising in the mean-field limit of large systems of bosons and explain its importance within the class of nonlinear Schrödinger equations. Of special interest to us is the Hartree equation with focusing nonlinearity (attractive two-body interactions). Rigorous results for the Hartree equation are presented concerning: 1) its derivation from the quantum theory of large systems of bosons, 2) existence and stability of Hartree solitons, and 3) its point-particle...
Osman, Frederick, Beech, Robert (2005)
Journal of Applied Mathematics and Decision Sciences
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Kovachev, Lubomir M. (2004)
International Journal of Mathematics and Mathematical Sciences
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Kovachev, Lubomir M. (2004)
International Journal of Mathematics and Mathematical Sciences
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Warminski, J., Kecik, K. (2006)
Mathematical Problems in Engineering
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Manevitch, L.I., Kovaleva, A.S., Manevitch, E.L. (2010)
Mathematical Problems in Engineering
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Yu N. Ovchinnikov, Israel Michael Sigal (1997-1998)
Séminaire Équations aux dérivées partielles
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We describe qualitative behaviour of solutions of the Gross-Pitaevskii equation in 2D in terms of motion of vortices and radiation. To this end we introduce the notion of the intervortex energy. We develop a rather general adiabatic theory of motion of well separated vortices and present the method of effective action which gives a fairly straightforward justification of this theory. Finally we mention briefly two special situations where we are able to obtain rather detailed picture...