On modulational instabilities in discretisations of the Korteweg-de Vries equation (Q1111407)

\textit{W. L. Briggs}, \textit{A. C. Newell}, and \textit{T. Sarie} [ibid. 51, 83- 106 (1983; Zbl 0512.65070)] have studied nonlinear instabilities in discretisations of the equation \(u_ t+(u+U)u_ x=0\), where U is a constant. They demonstrated that solutions of leap-frog discretisations of this equation could be destabilised by a dynamic process which can localise noise on the spatial grid. \textit{D. M. Sloan} and \textit{A. R. Mitchell} [ibid. 67, 372-395 (1986; Zbl 0605.65054)] examined these instabilities by considering perturbations of the basic solution which take the form of side-band Fourier modes. Here this latter work is extended to cover analogous discretisations of the Korteweg-de Vries equation.