Numerical solutions of the Korteweg-de Vries equation using the periodic scattering transform \(\mu\)-representation (Q919771)

A numerical procedure is developed, based on the periodic scattering transform, for determining the spatial and temporal evolution of solutions of the Korteweg-de Vries equation with periodic boundary conditions. In this approach solutions of KdV are found in terms of the ``\(\mu\)-representation''; the wave amplitude is given by a trace formula consisting of a linear superposition of hypoelliptic functions, governed by a system of nonlinear, ordinary differential equations. These equations are integrated numerically, using a second order Taylor series expansion with a variable step size.