VARIATIONAL APPROACH TO LANGMUIR-WAVES DESCRIBED BY THE ZAKHAROV EQUATIONS

Nonlinear modulational instability and the evolution of a pulse that is initially non-solitonic for Langmuir waves described by the Zakharov equations are considered. The average Lagrangian method has been used to derive the nonlinear dispersion relation for Stokes waves. It is found that the region of instability increases with the amplitude of the perturbed Langmuir field. The propagation of the pulse is studied with the help of the Rayleigh-Ritz optimization method. It is noted that the width of the pulse oscillates rapidly for high initial pulse velocity.