Solitons in the Korteweg-de Vries Equation

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 L${}^2$ error analysis demonstrated consistency between numerical methods of solving the KdV equation and analytical solutions.