Whitham Modulation Equations and Application to Small Dispersion Asymptotics and Long Time Asymptotics of Nonlinear Dispersive Equations

In this chapter we review the theory of modulation equations orWhitham equations for the travelling wave solution of KdV. We then apply the Whitham modulation equations to describe the long-time asymptotics and small dispersion asymptotics of the KdV solution.