The discrete logistic map was one of the first equations to be studied for
the production of chaos. We shall show that a soliton solution exists for t
he differential logistic equation when the output is the derivative of the
dependent variable rather than the variable itself. Furthermore, when the l
ogistic equation is solved using Euler's forward algorithm a transition fro
m a soliton solution to chaos exists and can be accurately predicted. The r
esults are used directly to design an electronic soliton generator.