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Trevor Caldwell

Picture of 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

Additional Materials

Poster