Nonlinear Time-Dependent Plasma Oscillations

Abstract

The Laplace transform technique employed by Landau to solve the problem of the first-order motions in an unbounded, rarified, electron plasma is modified to solve the problem to arbitrarily high order. The transforms of the $n\mathrm{th}$-order contributions are expressible in terms of convolution integrals involving only terms up to order $n-1\mathrm{}$. The method is applied to second order for the case of square-integrable disturbances.