Trevor Caldwell
Thesis
Nonlinear Wave Equations and Solitary Wave Solutions in Mathematical Physics
- Advisor
- Alfonso Castro
- Second Reader(s)
- Jon T. Jacobsen
Abstract
In this report, we study various nonlinear wave equations arising in mathematical physics and investigate the existence of solutions to these equations using variational methods. In particular, we look for particle-like traveling wave solutions known as solitary waves. This study is motivated by the prevalence of solitary waves in applications and the rich mathematical structure of the nonlinear wave equations from which they arise. We focus on a semilinear perturbation of Maxwell's equations and the nonlinear Klein–Gordon equation coupled with Maxwell's equations. Physical ramifications of these equations are also discussed.
Proposal
Solitary Wave Solutions in Modern Physics with Applications to Maxwell's Equations
