Wave interactions in the singular Zakharov system

Abstract

A multiscale perturbation method is used to derive solutions to the singular Zakharov equations governing the interaction of an acoustic wave with a plasma envelope. The method is described in general terms and then used to study two specific interactions. The first is that of a plasma standing wave with a monochromatic acoustic plane wave, the second is that of plasma soliton with a monochromatic plane wave. Systems of modulation equations governing the leading-order interactions and higher-order interactions are derived and solved. The higher-order interaction equations ultimately reduce to solving a Schrödinger eigenvalue problem that can be solved using hypergeometric functions. The solutions are examined for fixed time as ε is increased and for fixed ε as time evolves.