Nonlinear Schrödinger-Airy Equation in Sobolev Spaces of Low Regularity
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Date
2020
Authors
Sakayeva, Zhanna
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Sciences and Humanities
Abstract
The Nonlinear Schrödinger-Airy equation is one of the general examples
of dispersive nonlinear partial differential equations. It is commonly used to
characterize the nonlinear propagation of light pulses in optical fibers and is of
great importance in quantum mechanics. In this Capstone Project, we perform
the first steps to show that the solution satisfies a priori upper bound in terms
of the Hs(Sobolev Space) size of the initial data for -1/8 < s < 1/
4 . The result is weaker than the well-posedness. The Capstone Project provides a general scheme of the ideas for the problem described above.
Description
Keywords
partial differential equations. low regularity, fourier transform