Bilinear Transformation Method (Enhanced Edition‪)‬

A history of the development of the mathematics of solitons begins
in 1967 with a remarkable discovery by Gardner et al. [l] of an exact
method for solving the initial value problem of the Korteweg-de Vries
(KdV) equation. They reduced the nonlinear problem to the linear
one, which was well known as the Sturm-Liouville eigenvalue problem
characterized by the Schrodinger equation, and then discussed the
properties of the exact solution describing the interaction of solitons.