Abstract

This thesis investigates the effect of viscous damping on rogue wave formation and permanent downshift using the higher-order nonlinear Schrödinger equation (HONLS). The strength of viscous damping is varied and compared to experiments with only linear damped HONLS.

Stability analysis of the linear damped HONLS equation shows that instability stabilizes over time. This analysis also provides an instability criterion in the case of HONLS with viscous damping.

Numerical experiments are conducted in the two unstable mode regime using perturbations of the Stokes wave as initial data. With only linear damping permanent downshift is not observed and rogue wave formation is decreased. The addition of viscous damping leads to permanent downshift and a slight increase in rogue wave activity. Analysis of the energy and momentum gives a possible explanation for this behavior.

Thesis Completion

2022

Semester

Spring

Thesis Chair

Schober, Constance M.

Degree

Bachelor of Science (B.S.)

College

College of Sciences

Department

Mathematics

Language

English

Access Status

Campus Access

Length of Campus-only Access

1 year

Release Date

5-1-2023

Restricted to the UCF community until 5-1-2023; it will then be open access.

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