Abstract

Modulational instability occurs when small perturbations of a solution lead to exponential growth of the side bands. One equation used for studying modulational instability is the Nonlinear Schrodinger (NLS) equation. The NLS is a completely integrable nonlinear PDE which possesses a large class of unstable solutions. The simplest modulationally unstable solution of the NLS is the Stokes wave. In this thesis, we review the work of Ablowitz and Schober and explore the nearby states to the modulationally unstable plane wave.

Notes

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Graduation Date

2022

Semester

Summer

Advisor

Schober, Constance

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematical Science

Identifier

CFE0009151; DP0026747

URL

https://purls.library.ucf.edu/go/DP0026747

Language

English

Release Date

August 2027

Length of Campus-only Access

5 years

Access Status

Masters Thesis (Campus-only Access)

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Restricted to the UCF community until August 2027; it will then be open access.

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