Author ORCID Identifier
Date Available
7-24-2023
Year of Publication
2023
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Mathematics
First Advisor
Dr. Peter Perry
Abstract
We will prove scattering for the fifth-order Kadomtsev-Petviashvilli II (fifth-order KP-II) equation. The fifth-order KP-II equation is an example of a nonlinear dispersive equation which takes the form $u_t=Lu + NL(u)$ where $L$ is a linear differential operator and $NL$ is a nonlinear operator. One looks for solutions $u(t)$ in a space $C(\R,X)$ where $X$ is a Banach space. For a nonlinear dispersive differential equation, the associated linear problem is $v_t=Lv$. A solution $u(t)$ of the nonlinear equation is said to scatter if as $t \to \infty$, the solution $u(t)$ approaches a solution $v(t)$ to the linear problem in the Banach space $X$. Our work is based on the analysis of the third-order KP-II equation by Hadac, Herr, and Koch.
Digital Object Identifier (DOI)
https://doi.org/10.13023/etd.2023.304
Funding Information
This work was supported by the Fuoco Fellowship in 2022 and Graduate Scholars in Mathematics Fellowship in 2019-2021.
Recommended Citation
Schuetz, Camille, "A Scattering Result for the Fifth-order KP-II Equation" (2023). Theses and Dissertations--Mathematics. 103.
https://uknowledge.uky.edu/math_etds/103
