ABSTRACT
This chapter is concerned with the initial value problem for the Korteweg-deVries (KdV) equation. In the formulation of the KdV, solitons are negative waves traveling toward the right. The motivating problem is to identify those initial profiles or which one can prove existence of a classical solution by the inverse scattering method. The chapter provides a brief outline of the inverse scattering method and presents a slightly deeper review of the underlying scattering theory for the Schrödinger equation. It applies the results of the inverse scattering method to outline the solution of the initial value problem.
