Behaviour of slow Langmuir solitons

Zakharov's equations, describing the interaction of Langmuir waves and ion sound, are studied in the regime of low amplitude and wavenumber by means of an expansion in powers of the Mach number. A perturbed non-linear Schroedinger equation is derived, and shown to possess adiabatic invariants which are analogous to the conserved quantities of the unperturbed equation. One of these is constructed explicitly. (Auth.)