Well-Posedness of the Nonlinear Schrödinger Equation

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dc.contributor.authorOrumbayeva, Sara
dc.date.accessioned2019-08-08T08:36:13Z
dc.date.available2019-08-08T08:36:13Z
dc.date.issued2019-08-07
dc.description.abstractThe Nonlinear Schrödinger equation (NLSE) is a prototypical example of nonlinear partial differential equation. It is commonly used to describe propagation of light in nonlinear optical fibers and is of great importance in quantum mechanics. In this Capstone Project, we provide a complete proof of well-posedness, that is existence of a unique solution of the NLSE using one of the major mathematical techniques: the Banach fixed-point theorem. Both local and global results for inital data in L2(R) are obtained. Moreover, we briefly discuss possible extensions of the topic in terms of different function spaces, general nonlinearities and higher dimension.en_US
dc.identifier.citationOrumbayeva, S. (2019). Well-Posedness of the Nonlinear Schrödinger Equation. Nazarbayev University, School of Science and Technologyen_US
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/4094
dc.language.isoenen_US
dc.publisherNazarbayev University School of Science and Technologyen_US
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.subjectSchrodinger equationen_US
dc.subjectnonlinear Schrodinger equationen_US
dc.titleWell-Posedness of the Nonlinear Schrödinger Equationen_US
dc.typeCapstone Projecten_US
workflow.import.sourcescience

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