Published online by Cambridge University Press: 13 March 2009
Using the Zakharov equations in their Fourier-transformed form, we consider the development of the modulational instability (MI) both for the monochromatic and the finite-width cases. In the static approximation and considering a monochromatic Langmuir wave which is coupled only to a single pair of Stokes and anti-Stokes Langmuir perturbations, we show that the resultant set of equations is integrable and we discuss the analytical solution of these equations. We show how a finite-width driver will lead to a threshold for the MI. We compare our results with those obtained by other authors.