Solitons in the Korteweg-de Vries Equation
Abstract
We propose a numerical solution to the Korteweg-de Vries (KdV) equation using a Crank-Nicolson scheme, and compare its performance to the Fast Fourier Transform method. The properties and interactions of soliton solutions are further examined. Initial conditions were varied to analyse soliton formation in the resulting system. Performing an L2 error analysis demonstrated consistency between numerical methods of solving the KdV equation and analytical solutions.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.