Nonlinear wave modulations in plasmas

Abstract

A review of the generic features as well as the exact analytical solutions of coupled scalar field equations governing nonlinear wave modulations in plasmas is presented. Coupled sets of equations like the Zakharov system, the Schrödinger-Boussinesq system and the Schrödinger-KDV system are considered. For stationary solutions, the latter two systems yield a generic system of a pair of coupled, ordinary differential equations with many free parameters. Different classes of exact analytical solutions of the generic system which are valid in different regions of the parameter space are obtained. The generic system is shown to generalize the Hénon-Heiles equations in the field of nonlinear dynamics to include a case when the kinetic energy in the corresponding Hamiltonian is not positive definite. The relevance of the generic system to other equations like the self-dual Yang-Mills equations, the complex KDV equation and the complexified classical dynamical equations is also pointed out.