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Existence and Stability of Vortex Solutions of Certain Nonlinear Schrodinger Equations

dc.contributor.advisorPego, Robert Len_US
dc.contributor.authorKollar, Richarden_US
dc.date.accessioned2004-06-04T05:52:24Z
dc.date.available2004-06-04T05:52:24Z
dc.date.issued2004-05-04en_US
dc.identifier.urihttp://hdl.handle.net/1903/1488
dc.description.abstractThe nonlinear Schrodinger equation models a wide variety of different physical phenomena ranging from nonlinear optics, water waves, magnetization of ferromagnets to Bose-Einstein condensates (BEC). The structure of the equation supports existence of topologically non-trivial solutions - vortices. Surprisingly, we demonstrate that the Landau-Lifshitz magnetization equation which is formally also a nonlinear Schrodinger equation does not admit such solutions. On the other hand, the contrary is true for the Gross-Pitaevskii equation which describes the mean-field approximation of BEC. We investigate stability of vortex solutions by means of a very reliable, sensitive and robust technique - the Evans function. This method, although limited to two dimensions, allows us to study rotating axisymmetric BEC for large particle numbers which can be unattainable by other means.We found a singly-quantized vortex linearly stable.The linear stability of multi-quantized vortices depends on the diluteness of a condensate, with alternating intervals of stability and instability. This work justifies previous results in the literature obtained by less reliable methods and opens up a few interesting questions.en_US
dc.format.extent1918458 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.titleExistence and Stability of Vortex Solutions of Certain Nonlinear Schrodinger Equationsen_US
dc.typeDissertationen_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.contributor.departmentMathematicsen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledPhysics, Condensed Matteren_US
dc.subject.pqcontrolledPhysics, Electricity and Magnetismen_US
dc.subject.pquncontrolledVortex solutiotionsen_US
dc.subject.pquncontrollednonlinear Schrodinger equationen_US
dc.subject.pquncontrolledBose-Einstein condensatesen_US
dc.subject.pquncontrolledLandau-Lifshitz equationen_US
dc.subject.pquncontrolledmagnetization equationen_US
dc.subject.pquncontrolledEvans functionen_US


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