Nonlinear Responses of Dispersive Media. II. A Stability of Stationary Solutions to the KdV Equation with a Sinusoidal Force

Abstract

In the present paper a Korteweg-de Vries equation with a sinusoidal force and a small coefficient of dispersion is considered, and by means of numerical computations it is shown that a class of periodic stationary solutions, found in a previous paper and interpreted as describing a balance between the nonlinearity and the external force, is neutrally stable.