A Gentle Introduction to the Korteweg-de Vries equation, Solitary Waves, and Applied Partial Differential Equations

Abstract

The study of partial differential equations can be a daunting one, yet they have countless applications across diverse subjects of inquiry. We introduce one such application here with an aim to illustrate that, contrary to any appearance of being arcane and impenetrable, important partial differential equations may be presented and made accessible to a general audience. Here we introduce the Korteweg-de Vries equation, explain its historical development and significance, illustrate some properties, derivations, solutions, and applications, and in particular its relevance to the study of solitary waves and the more general class of objects known as Solitons. By illuminating the elegance of partial differential equations and demonstrating that they are not an intimidating subject, we hope to foster greater appreciation for the them, while providing an idea of just what the study of partial differential equations entails to those who may be interested in taking up the study of partial differential equations themselves.

Discipline: Mathematics

Faculty Mentor: Dr. Ion Bica