Several problems in nonlinear Schrödinger equations

Author

Tim Van Hoose

Keywords and Phrases

Nonlinear partial differential equations

Abstract

“We study several different problems related to nonlinear Schrödinger equations….

We prove several new results for the first equation: a modified scattering result for both an averaged version of the equation and the full equation, as well as a set of Strichartz estimates and a blowup result for the 3d cubic problem.

We also present an exposition of the classical work of Bourgain on invariant measures for the second equation in the mass-subcritical regime”--Abstract, page iv.

Advisor(s)

Murphy, Jason

Committee Member(s)

Han, Daozhi
Singler, John R.

Department(s)

Mathematics and Statistics

Degree Name

M.S. in Applied Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Spring 2022

Journal article titles appearing in thesis/dissertation

• Modified scattering for a dispersion-managed nonlinear Schrödinger equation
• Well-posedness and blowup for the dispersion-managed nonlinear Schrödinger equation

Pagination

ix, 102 pages

Note about bibliography

Includes bibliographic references.

Rights

© 2022 Timothy Robert Van Hoose, All rights reserved.

Document Type

Thesis - Open Access

File Type

text

Language

English

Thesis Number

T 12138

Recommended Citation

Van Hoose, Tim, "Several problems in nonlinear Schrödinger equations" (2022). Masters Theses. 8100.
https://scholarsmine.mst.edu/masters_theses/8100