Date of Award
5-31-2012
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
First Thesis Advisor
Alfonso Castro
Second Thesis Advisor
Jon T. Jacobsen
Rights Information
© Trevor Caldwell
Terms of Use & License Information
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.
Recommended Citation
Caldwell, Trevor, "Nonlinear Wave Equations and Solitary Wave Solutions in Mathematical Physics" (2012). HMC Senior Theses. Paper 32.
http://scholarship.claremont.edu/hmc_theses/32