Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation

An explicit nonlinear transformation relating solutions of the Korteweg-de Vries equation and a similar nonlinear equation is presented. This transformation is generalized to solutions of a one-parameter family of similar nonlinear equations. A transformation is given which relates solutions of a ``forced'' Korteweg-de Vries equation to those of the Korteweg-de Vries equation.