Nonlinear stability analysis of electrified liquid jet under the influence of a uniform axial periodic electric field

The parametric excitation of surface waves on a liquid jet in the presence of an axial periodic electric field is investigated . The method of multiple scales is used to derive and analyze the necessary and sufficient conditions for stability. Owing to the periodicity, resonant cases appear .Two parametrically nonlinear Schrodinger equations are obtained for the resonance cases . The formula for the surface elevation is derived in each case . A classical nonlinear Schrődinger equation is deduced for the non -resonance case . Investigation of the stability criterion by nonlinear perturbation shows that the periodic electric field has a stabilizing effect.