Soliton Solution for the Korteweg-de Vries Equation

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, wherem 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