ABSTRACT
This chapter aims to apply known results written in the monograph about the inverse scattering problem for the Schrodinger equation on the half-line to solving the initial-boundary value problem (IBVP) for the Korteweg-de Vries (KdV) equation. The KdV equation is the generic equation for the study of weakly nonlinear long waves. It arises in physical systems, which involve a balance between weak nonlinearity and weak dispersion at leading order. The KdV equation arises in many physical situations, such as surface water waves, internal waves in density-stratified fluid, plasma waves, Rossby waves and magma flow. The chapter describes the known results of the direct and inverse scattering problem on the half-line associated with the IBVP for the KdV equation on the positive quarter-plane.
