Solitary Wave Solutions to the Fifth-Order KdV Equation
Date of Creation
2014
Document Type
Departmental Honors Thesis - Restricted Access
Department
Mathematics
First Advisor
Steven Levandosky
Abstract
The Kortweg-deVries equation is a mathematical model for water waves in shallow surfaces and we study solitary wave solutions to this equation. We investigate the stability of traveling wave solutions to the third-order equation, and prove the existence of solutions to fifth-order equation for a particular inhomogeneous, nonlinear term. The inhomogeneity restricts our methods for solving the partial differential equation in terms of locating critical points through functional analysis. We use a modified Mountain Pass Theorem to successfully prove the existence of these critical points, and further, the existence of solitary wave solutions to the fifth-order KdV equation.
Recommended Citation
Wilkman, Alison, "Solitary Wave Solutions to the Fifth-Order KdV Equation" (2014). Math and Computer Science Honors Theses. 43.
https://crossworks.holycross.edu/math_honor/43