Well-Posedness of the Nonlinear Schrödinger Equation
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Date
2019-08-07
Authors
Orumbayeva, Sara
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Science and Technology
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.
Description
Keywords
Schrodinger equation, nonlinear Schrodinger equation
Citation
Orumbayeva, S. (2019). Well-Posedness of the Nonlinear Schrödinger Equation. Nazarbayev University, School of Science and Technology