Soliton Solution for the Korteweg-de Vries Equation

Authors

  • Ana Mucalica MacEwan University

DOI:

https://doi.org/10.31542/muse.v6i1.2262

Abstract

Korteweg de Vries (KdV) model is considered quintessential in modeling the surface gravity water waves in shallow water. In this project, we are interested in starting from the Elliptic Jacobian Functions, and performing a complete analysis of these functions to discover that one can recover the soliton in the particular case,  when m approaches 1, where
m is a parameter between 0 and 1 in the definition of the Elliptic Jacobian Functions.


This analysis will provide us with an understanding of cnoidal periodic waves and how, through them, we can derive the soliton solution. Finally, this project grants readers a deeper understanding of the origin of solitons and their applications in water wave theory.

Downloads

Published

2022-05-30

How to Cite

Mucalica, A. (2022). Soliton Solution for the Korteweg-de Vries Equation. MacEwan University Student EJournal, 6(1). https://doi.org/10.31542/muse.v6i1.2262

Issue

Section

Arts and Sciences - Science