Abstract
A charge-free surface separating two semi-infinite dielectric fluids influenced by a tangential periodic electric field is subjected to nonlinear deformations. We use the method of multiple scales in order to solve nonlinear equations. In the first order problem, we obtain Mathieu's differential equation. In the second order problem, we obtain the nonhomogenous Mathieu equation and we use the method of multiple scales to obtain a sequence of equations. In the third order problem, we obtain a differential equation of the second order of periodic coefficients. Also, we obtain a formula for surface elevation. The stability conditions are determined.
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