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Well-Posedness of the Nonlinear Schrödinger Equation

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dc.contributor.author Orumbayeva, Sara
dc.date.accessioned 2019-08-08T08:36:13Z
dc.date.available 2019-08-08T08:36:13Z
dc.date.issued 2019-08-07
dc.identifier.citation Orumbayeva, S. (2019). Well-Posedness of the Nonlinear Schrödinger Equation. Nazarbayev University, School of Science and Technology en_US
dc.identifier.uri http://nur.nu.edu.kz/handle/123456789/4094
dc.description.abstract The 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.language.iso en en_US
dc.publisher Nazarbayev University School of Science and Technology en_US
dc.rights Attribution-NonCommercial-ShareAlike 3.0 United States *
dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/us/ *
dc.subject Schrodinger equation en_US
dc.subject nonlinear Schrodinger equation en_US
dc.title Well-Posedness of the Nonlinear Schrödinger Equation en_US
dc.type Capstone Project en_US
workflow.import.source science

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