Cold Plasma Oscillations: An Exact Solution of the Non Linear Equations

The one dimensional nonlinear hydrodynamic equations describing longitudinal cold plasma oscillations are studied by the classical Lagrangian-Euler method. A new method to invert the solutions from Lagrangian to Euler description is introduced. It is also shown in this paper that this method is capable of yielding results identical to those from KBM perturbation to second order of approximation. The new method, however, produces higher order approximations much more rapidly.