ABSTRACT
This chapter provides a practical treatment of the theory of Korteweg-de Vries (KdV) solitons and includes the key derivations and references to the literature. It looks at the cnoidal and solitary wave solutions of the KdV equation. The solitary wave solution propagates through a linear medium and is shaped by a non-linear saturable absorber and a low-pass filter to create the sech shaped pulse. The chapter illustrates the fascinating dynamics of soliton collisions. It presents the fundamental derivations of the KdV soliton and its steady-state solution. The derivation of the periodic solution to the KdV equation utilizes elliptic functions, which are unfamiliar to most scientists and engineers. They represent solutions to elliptic integrals which appear in the derivations of many physical systems which have elliptic geometry. thus demonstrating the connection of elliptic functions to standard and hyperbolic trigonometric functions.
